#How to find the sum of all numbers from 1 number to another

146 messages · Page 1 of 1 (latest)

small gorge
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For instance the sum of all positive natural numbers from 3 to 1000

daring fulcrumBOT
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small gorge
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3 + 4 + 5 + 6 + 7 + ..... + 999 + 1000

compact sapphire
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search up arithmetic series

small gorge
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for certain numbers

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what to do then

foggy coral
small gorge
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(2 + 499)/2

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x 499

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Gives a decimal answer

foggy coral
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$S=\frac{n}{2}(2a+(n-1)d)$

nova ridgeBOT
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;( | 追放された興奮

1245133657690214403.png
small gorge
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then wtf does this do

image.png
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why are there two different equations

foggy coral
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are you, like, calculating it right

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that too

small gorge
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yeah

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501/2

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is a decimal

foggy coral
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it works

small gorge
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Ok

foggy coral
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where are you getting 501

small gorge
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a1 = 2

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an = 499

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do that

foggy coral
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multiply by n?

small gorge
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yeah

foggy coral
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which is an even number?

small gorge
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(2 + 499)/2

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x 499

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is a decimal

foggy coral
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which produces an integer result?

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n=498

small gorge
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No

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It equals 499

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Not 498

foggy coral
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are you okay.

small gorge
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Stop changing my values to gaslight me

foggy coral
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count your numbers again.

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i will calculate it right now

small gorge
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n = 499

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in this case

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do it

foggy coral
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,w 2+3+4...499

nova ridgeBOT
foggy coral
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...

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,w \sum_{n=2}^{499} n

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i told you.

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it’s an integer.

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count your numbers properly

small gorge
foggy coral
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when you have a sequence starting from a and ending at b, the amount of numbers in the sequence is b-a+1

small gorge
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NO not

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3 - 499

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2 - 499

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  • as in to
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"-" as in to

foggy coral
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okay

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still

nova ridgeBOT
small gorge
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"Still" thats a different value

foggy coral
small gorge
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How do I use this

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Because its giving me a decimal answer and it shouldnt

small gorge
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Im trying to find the sum of 2 to 499

foggy coral
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oh my

small gorge
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2 + 3 + .... + 499

foggy coral
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did i not explain this already?

small gorge
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a1 = 2

an = 499

foggy coral
small gorge
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((2+499)/2) x 499 = 124999.5

foggy coral
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dude.

small gorge
foggy coral
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I quite literally just provided a method to count it

small gorge
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Why are you being a jerk

foggy coral
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if it starts and a and ends at b, the amount of terms in the sequence is b-a+1

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so if it starts at 2 and ends at 499, what is the amount of terms?

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@small gorge

small gorge
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or 501

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idk

foggy coral
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fine, i’ll put it better

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the amount of terms is $a_n-a_1+1$

nova ridgeBOT
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;( | 追放された興奮

1245133657690214403.png
solid hemlock
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sum of n from n = a to n= b, where 0<a<b, a,b are integers.

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This is equal to sum of n from n = 1 to n = b which b(b+1)/2 but you subtract the sum of n from n =1 to n = a which is a(a+1)/2. So, b(b+1)/2 - a(a+1)/2, when factoring out difference of two squares is (a+b+1)(b-a)/2

celest marsh
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dont randomly drop a solution when op has already made progress

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this confuses people

celest marsh
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how many numbers are there from 1 to 3 inclusive?

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are there 3-1 = 2?

compact sapphire
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it should be (2+499) * 498 /2

celest marsh
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mistake is not knowing number of numbers thing

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which has been explained but idk if op got it

compact sapphire
# celest marsh

my mistake; i did not see that - but there are 498 numbers

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ok

pure arrow
celest marsh
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its the sum of integers lol

pure arrow
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Or, at least, you make a good point, it's always an integer for a series of integers.

pure arrow
foggy coral
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i just went to sleep cause i had stuff to do today

true imp
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So the amount of terms is
$a_n-a_1+1$
We can express the formula of the summation of terms as:
$\frac{a_n-a_1+1}{2}\cdot(a_1+a_n)$

nova ridgeBOT
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denzio321

733298332809691239.png
true imp
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So if $a_n-a_1+1$ is not divisble by 2

nova ridgeBOT
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denzio321

733298332809691239.png
true imp
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Then $a_n-a_1$ is divisble by 2

nova ridgeBOT
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denzio321

733298332809691239.png
true imp
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So then $a_n+a_1$ is divisble by 2

nova ridgeBOT
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denzio321

733298332809691239.png
true imp
pure arrow
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The amount of terms is... n.

foggy coral
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(and also OP doesn’t understand that)

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for some reason

pure arrow
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And considering before that we were talking about the sum of an arbitrary algebraic series...

foggy coral
pure arrow
foggy coral
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it’s whatever though

foggy coral
pure arrow
foggy coral
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i get that n=length, but OP things that n=a_n

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or some other number

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it’s not really incorrect when OP’s fundamental understanding is also incorrect

pure arrow
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The problem is a lack of specificity. That's the correct way to count the number of integers in a bounded interval, but not to count the number of terms in an algebraic sequence.

foggy coral
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i guess so

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still i’m trying to fix an underlying problem

pure arrow
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And I think the way to do that is to be more specific.

foggy coral
pure arrow
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Half the reason OP is confused seems to be because they don't know how to draw these kinds of distinctions.

turbid lynxBOT
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@small gorge

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