Series

[empty lark]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules. If there is a conflict amongst multiple helpers feel free to ping “Helper Mod”
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[crimson dragon]

well, for starters, lets split up the sum

$\sum_{r=1}^{12} 3r^2+\sum_{r=1}^{12} 8r+\sum_{r=1}^{12} 3+k\sum_{r=1}^{12} 2^{r-1}=3520$

[slim veldt]

;( | 追放された興奮

[terse spear]

yupp i agree

im not sure how to do the one with the k with 2^r-1 but i do know the others

[crimson dragon]

2^[r-1} is just a geometric series

[terse spear]

but i dont understand what would i do with it?

[crimson dragon]

$\sum_{k=1}^{n} ar^k= \frac{a(1-r^n)}{1-r}$

[terse spear]

ahh

i dont think ive been taught that yet lol, but ill try anyways lol

[crimson dragon]

yes

it should be taught.

just remember

[slim veldt]

;( | 追放された興奮

[crimson dragon]

2^{r-1}=2^r * 1/2

[terse spear]

so where there is a r in the fraction on the right, do i sub in 1/2n(n+1)?

[crimson dragon]

wdym

[terse spear]

im not sure, its my first time seeing smthing like that

[crimson dragon]

hmm

[terse spear]

do u think i should just skip this question?

[crimson dragon]

no, it is achievable

here, let me simplify

[terse spear]

okii

[crimson dragon]

$\sum_{r=1}^{12} \frac{2^r}{2}$

[slim veldt]

;( | 追放された興奮

[crimson dragon]

we can simplify that for 2^{r-1}

?

hello?

[terse spear]

ah apologies, i understand

im not completely sure how you manipulated 2^r-1 in that form

[crimson dragon]

i used an exponent law

$a^{b-c}=\frac{a^b}{a^c}$

[slim veldt]

;( | 追放された興奮

[terse spear]

oh-

okk

[crimson dragon]

sorry

i have some work to do

[terse spear]

wait i think ik how to do it now

[crimson dragon]

i will be back in like another hour

[terse spear]

nws, i think i can do the question 😄

tysm for ur help