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Can someone help with this? :) It is posted below in the comment section so I can use the Equation editor.

Mathematics
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|dw:1362285707700:dw|\[\Sigma \]
Find the sum of the arithmetic series! Pleassse help:)
\(\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}\) and a constant (here, 5) can be taken out of sum sign... :)

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Other answers:

Where r we getting this formula? I'm confused where to start
thats a standard formula that can be used.
do you want a formula for sum of terms in arithmetic series ? its equivalent to this formula
Deriving the formula for an arithmetic series?
Yes that is the formula for the arithmetic series. Where do we go from there?:)
to find the sum?
Well, maybe best to use this formula instead \[\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}\] It's simpler :D
So anyway, this sum is just... |dw:1362286375802:dw| right?
ok, i'll mention the sum of arithmetic series formula also, then you choose which one you wanna use, the series will be 5,10,15,20,.... right ? (with n= 100 terms) he 1st term a1 = 5 and there's a common difference of d=5 then the sum formula is : \(S_n = (n/2)(2a+(n-1)d)\)
terenzreignz...how do you get these expanded form answer? Can u explain that? sorry
It is isn't the right answer in the back of the book
That's just kind of the definition. Or you could say the sigma notation is a compact form of the sum. \[\huge \sum_{k=1}^n=1+2+3+...+(n-1)+n\] Basically adding all integers starting at 1 to n.
\[\huge \sum_{k=1}^nk=1+2+3+...+(n-1)+n\] Bloody typo, sorry :)
So anyway, we can rearrange...|dw:1362286994735:dw|
And notice that these terms...|dw:1362287037927:dw| When added, they all equal n+1
what is the final answer? the answer is supposed to be 25,250...I just don't know how to get it
did you try any one of the 2 formula i gave u ??
Going back to hartnn's response near the beginning. This is like the only formua I'm understanding how to do. \[S _{100}= (100(5 + ?))/2\] I'm just confused how to get that number I didn't fill in? It's supposed to be \[t _{n}\] (which is last term)
Anyone?
oh, you need last term ? the general term is 5k to get last term, just put k=100 in general term so, what u get as last term ?
So i fill in that question mark spot with 100? Im not sure
general term =5k with k=100, last term = 5*100 = 500 -_-
To clarify, this is the formula I am using. \[S _{n}=\frac{ n(t _{1}+ t _{n} )}{ 2 }\]
wait how does k =100 again?
yup, thats the only other i didn't mention :P because you are summing from k=1 (which is 1st term) to k=100 (WHICH IS LAST TERM)
lower limit givs first term, upper limit gives last term
ok so 100 is the last term... And why do we multiply it by 5?
last value of k is 100 general term = 5k so last term = 5*100
and the difference between the numbers would be five right? or is it something else
yes, common difference = 2nd term -1st term = 3rd term -2nd term =.... = 10-5 = 15-10 =.... = 5 but thats not required for the formula you are using
Oh ok that makes sense now. Maybe you should help me on other problems I post. Your a good help!
ok, sure, but did u get 25250 for this one ?
Oh wait quick question! What was \[t _{1}\] in this equation
t1 is the 1st term index represents which term
tn is the n'th term
the index is which part again?
index is written as subscript \(\huge t_n\) here n is index and represent which term, t1 = 1st term, t2 =2nd term, and so on
so t1 is 5
yup. as 5 is the 1st term
any more doubts ?
ok im sorry so I'm trying to solve it on paper. And I'm confused again.. how did we get \[t _{n}\] in the formula
oh wait my bad! i got it
you mean in \(S_n = n (t_1+t_n)/2\) thats a general formula, do you want a derivation of this ?
oh u got it ? good :)
What would happen when I solve for \[t _{n}\] in an equation where n did not equal 1 and it equaled something else?
didn't get your question ? do u have specific example for that ? say, if you want to find \(t_5\), then u put n=5 in general term tn
|dw:1362289579021:dw| Like this. N does not equal 1
i think u have made up this question ? or is it from your book/notes ?
I made it up
here Ill give you one from the book. |dw:1362289721775:dw|
thats 30- m by the way. It kinda got cut off
so, here your 1st term will start from m=10 in 30-m and last term you'll get by putting m=20 in 30-m
so how would i get \[t _{n}\]
tm = last term, last m =30 so to get last term tm, put m=30 in general term 30-m is this confusing ?
kinda
general term tm =30-m fist term t10 = 30-10 (put m=10) last term t20 = 30-20 (put m=20)
so I would do 30 -10 first , and when do I do the 20? i dont know if that makes sense
it doesn't -_-
ok lets not do this problem.. Ill ask my teacher on monday..
you have formula, you have n, you have 1st term, u have last term....just plug in values! ohh..ok, as u wish
Ill be posting other problems so u may help me if u want

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