Summation Notation | Mathematics | Page 1

silent epoch Oct 22, 2023, 3:53 AM

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acoustic pikeBOT Oct 22, 2023, 3:53 AM

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silent epoch

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agile pelican Oct 22, 2023, 4:26 AM

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The sequence is -2,-8,-32, …

silent epoch Oct 22, 2023, 4:54 AM

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$S_n$ = $\frac{a_1(1-r^n)}{1-r}$

gray vigilBOT Oct 22, 2023, 4:54 AM

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xNiden

silent epoch Oct 22, 2023, 4:57 AM

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Ima get back to this

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$a_n = a_1r^{n-1}$

gray vigilBOT Oct 22, 2023, 4:58 AM

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xNiden

agile pelican Oct 22, 2023, 5:18 AM

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Find the number of term first

winter sigil Oct 22, 2023, 6:23 AM

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$\sum_{r=0}^{n} (-2 \cdot 4^r)$

gray vigilBOT Oct 22, 2023, 6:23 AM

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Okkayow

winter sigil Oct 22, 2023, 6:26 AM

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to solve for n im pretty sure
-2 x 4^n = -32768
solve for n then put it into summation

silent epoch Oct 22, 2023, 8:09 AM

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mb

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im back now

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I was thinking like $a_1 = -2$ then $r = *4$

gray vigilBOT Oct 22, 2023, 8:11 AM

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xNiden

silent epoch Oct 22, 2023, 8:12 AM

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then if we use $a_n = a_1r^{n-1}$

gray vigilBOT Oct 22, 2023, 8:12 AM

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xNiden

silent epoch Oct 22, 2023, 8:14 AM

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we'll make n = -32768

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so

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$-32768 = -2 (4)^{n-1}$

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hm

young canopy Oct 22, 2023, 8:15 AM

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No

gray vigilBOT Oct 22, 2023, 8:15 AM

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xNiden

young canopy Oct 22, 2023, 8:16 AM

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Yes

silent epoch Oct 22, 2023, 8:16 AM

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then we wanna divide it right?

young canopy Oct 22, 2023, 8:16 AM

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Yes

silent epoch Oct 22, 2023, 8:16 AM

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ok

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that would be $16384 = 4^{n-1}$

gray vigilBOT Oct 22, 2023, 8:17 AM

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xNiden

young canopy Oct 22, 2023, 8:17 AM

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Yes

silent epoch Oct 22, 2023, 8:18 AM

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then um idk from here

young canopy Oct 22, 2023, 8:19 AM

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Do you know about logarithm?

silent epoch Oct 22, 2023, 8:19 AM

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yeah we take ln of both sides?

young canopy Oct 22, 2023, 8:19 AM

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Well not ln

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Take log base 4

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Because in the right you have a 4^, and they'll nicely simplify

silent epoch Oct 22, 2023, 8:20 AM

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Ah I see

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,calc log_4(16384)

gray vigilBOT Oct 22, 2023, 8:20 AM

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The following error occured while calculating:
Error: Undefined function log_4

young canopy Oct 22, 2023, 8:20 AM

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Hmm

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,w log base 4 of 16384

gray vigilBOT Oct 22, 2023, 8:21 AM

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Results provided by WolframAlpha

Click here to refine your query online
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silent epoch Oct 22, 2023, 8:23 AM

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OH

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oh

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oops

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i see

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alright

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so then

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it would be $7 = n-1$

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right?

gray vigilBOT Oct 22, 2023, 8:28 AM

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xNiden

silent epoch Oct 22, 2023, 8:28 AM

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since we did log

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or no

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because if we do log both sides then this should be right if im not wrong.

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hmm

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then n would equal 8

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n= 8

tulip reef Oct 22, 2023, 8:55 AM

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correct

tulip reef Oct 22, 2023, 8:56 AM

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silent epoch $S_n$ = $\frac{a_1(1-r^n)}{1-r}$

so use this

silent epoch Oct 22, 2023, 8:56 AM

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$S_n$ = $\frac{-2(1-4^8)}{1-4}$

gray vigilBOT Oct 22, 2023, 8:57 AM

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xNiden

silent epoch Oct 22, 2023, 8:59 AM

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then we can just flip it by multiplying both num and denom by -1 to make it $S_n$ = $\frac{-2(4^8-1)}{4-1}$

gray vigilBOT Oct 22, 2023, 8:59 AM

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xNiden

silent epoch Oct 22, 2023, 8:59 AM

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then $S_n$ = $\frac{-2(65535)}{3}$

gray vigilBOT Oct 22, 2023, 8:59 AM

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xNiden

silent epoch Oct 22, 2023, 9:01 AM

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then this would be

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,calc -2(65535)/3

gray vigilBOT Oct 22, 2023, 9:01 AM

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Result:

-43690

silent epoch Oct 22, 2023, 9:03 AM

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got it

silent epoch Oct 22, 2023, 9:32 AM

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$S_{oo} = \frac{a_1}{1-r}$

gray vigilBOT Oct 22, 2023, 9:33 AM

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xNiden

silent epoch Oct 22, 2023, 9:33 AM

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alr wtv

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anyways

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$S = \frac{5}{1-\frac{2}{7}}$

gray vigilBOT Oct 22, 2023, 9:34 AM

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xNiden

silent epoch Oct 22, 2023, 9:34 AM

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$S = \frac{5}{\frac{5}{7}} = 5 * \frac{7}{5}$

gray vigilBOT Oct 22, 2023, 9:35 AM

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xNiden

silent epoch Oct 22, 2023, 9:35 AM

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$S = 7$

gray vigilBOT Oct 22, 2023, 9:36 AM

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xNiden

silent epoch Oct 22, 2023, 9:39 AM

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$5+\frac{10}{7}+\frac{20}{49}+\frac{40}{343}$

gray vigilBOT Oct 22, 2023, 9:39 AM

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xNiden

silent epoch Oct 22, 2023, 9:39 AM

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mm

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its getting closer to 0

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alright ima do more later

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feel free to correct me if im wrong.

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S = 7

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7 is the answer

silent epoch Oct 22, 2023, 4:13 PM

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r= 0.4

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$S = \frac{-2}{1.4}$

gray vigilBOT Oct 22, 2023, 4:14 PM

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xNiden

silent epoch Oct 22, 2023, 4:15 PM

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$S = \frac{-2}{0.6}$

gray vigilBOT Oct 22, 2023, 4:15 PM

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xNiden

silent epoch Oct 22, 2023, 4:16 PM

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$S = -2*.6= -1.2$

gray vigilBOT Oct 22, 2023, 4:16 PM

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xNiden

silent epoch Oct 22, 2023, 4:17 PM

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hm

dapper shuttle Oct 22, 2023, 4:30 PM

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you need common ratio and first term
so think about what is multiples to get from 2 to -0.8 and -0.8 to 0.32, if these are different I suppose there’s no pattern?

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@silent epoch ^

silent epoch Oct 22, 2023, 4:32 PM

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mm

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I couldn't figure out what r equals

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I'll do it again ina bit

tulip reef Oct 22, 2023, 4:38 PM

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r = -0.4
cuz 0.8/(-2) = -0.4

silent epoch Oct 22, 2023, 4:49 PM

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yeah i think that's what I did

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so then i was correct

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then where did i mess up my calculations?

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$S = \frac{-2}{1.4}$

gray vigilBOT Oct 22, 2023, 4:51 PM

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xNiden

silent epoch Oct 22, 2023, 4:51 PM

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I think i found my mistake

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ima try it

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ah i got it

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simple mistake

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$S = \frac{-10}{7}$

gray vigilBOT Oct 22, 2023, 4:53 PM

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xNiden

silent epoch Oct 23, 2023, 5:14 AM

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$S= \frac{1}{1-\frac{1}{5}}$

gray vigilBOT Oct 23, 2023, 5:14 AM

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xNiden

silent epoch Oct 23, 2023, 5:15 AM

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$S= \frac{1}{\frac{4}{5}}$

gray vigilBOT Oct 23, 2023, 5:15 AM

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xNiden

silent epoch Oct 23, 2023, 5:16 AM

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$S= 1*{\frac{5}{4}}$

gray vigilBOT Oct 23, 2023, 5:17 AM

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xNiden

silent epoch Oct 23, 2023, 5:17 AM

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$S = \frac{5}{4}$

gray vigilBOT Oct 23, 2023, 5:17 AM

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xNiden

silent epoch Oct 23, 2023, 5:24 AM

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$\left(-\frac{1}{5}\right)^0 + \left(-\frac{1}{5}\right)^1 + \left(-\frac{1}{5}\right)^2 + \left(-\frac{1}{5}\right)^3 + \dots$

dapper shuttle Oct 23, 2023, 5:26 AM

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think about your first term and your common ratio

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wow the 0 is high up

gray vigilBOT Oct 23, 2023, 5:27 AM

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xNiden

silent epoch Oct 23, 2023, 5:27 AM

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there we are

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ok so then this =

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$1 - \frac{1}{5} + \frac{1}{25} - \frac{1}{125} + \dots$

gray vigilBOT Oct 23, 2023, 5:29 AM

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xNiden

silent epoch Oct 23, 2023, 5:32 AM

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$S = \frac{1}{1-\left(-\frac{1}{5}\right)}}$

gray vigilBOT Oct 23, 2023, 5:34 AM

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xNiden
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

silent epoch Oct 23, 2023, 5:35 AM

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$S = \frac{1}{1+\frac{1}{5}}}$

gray vigilBOT Oct 23, 2023, 5:35 AM

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xNiden
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

silent epoch Oct 23, 2023, 5:39 AM

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$S = \frac{5}{6}$

gray vigilBOT Oct 23, 2023, 5:39 AM

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xNiden

silent epoch Oct 23, 2023, 7:52 AM

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+close

#Summation Notation