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

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sparky16Best ResponseYou've already chosen the best response.0
dw:1362285707700:dw\[\Sigma \]
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
Find the sum of the arithmetic series! Pleassse help:)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
\(\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}\) and a constant (here, 5) can be taken out of sum sign... :)
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
Where r we getting this formula? I'm confused where to start
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
thats a standard formula that can be used.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
do you want a formula for sum of terms in arithmetic series ? its equivalent to this formula
 one year ago

terenzreignzBest ResponseYou've already chosen the best response.0
Deriving the formula for an arithmetic series?
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
Yes that is the formula for the arithmetic series. Where do we go from there?:)
 one year ago

terenzreignzBest ResponseYou've already chosen the best response.0
Well, maybe best to use this formula instead \[\huge \sum \limits_{k=1}^nk = \dfrac{n(n+1)}{2}\] It's simpler :D
 one year ago

terenzreignzBest ResponseYou've already chosen the best response.0
So anyway, this sum is just... dw:1362286375802:dw right?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
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 : \(S_n = (n/2)(2a+(n1)d)\)
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
terenzreignz...how do you get these expanded form answer? Can u explain that? sorry
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
It is isn't the right answer in the back of the book
 one year ago

terenzreignzBest ResponseYou've already chosen the best response.0
That's just kind of the definition. Or you could say the sigma notation is a compact form of the sum. \[\huge \sum_{k=1}^n=1+2+3+...+(n1)+n\] Basically adding all integers starting at 1 to n.
 one year ago

terenzreignzBest ResponseYou've already chosen the best response.0
\[\huge \sum_{k=1}^nk=1+2+3+...+(n1)+n\] Bloody typo, sorry :)
 one year ago

terenzreignzBest ResponseYou've already chosen the best response.0
So anyway, we can rearrange...dw:1362286994735:dw
 one year ago

terenzreignzBest ResponseYou've already chosen the best response.0
And notice that these terms...dw:1362287037927:dw When added, they all equal n+1
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
what is the final answer? the answer is supposed to be 25,250...I just don't know how to get it
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
did you try any one of the 2 formula i gave u ??
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
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)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
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 ?
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
So i fill in that question mark spot with 100? Im not sure
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
general term =5k with k=100, last term = 5*100 = 500 _
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
To clarify, this is the formula I am using. \[S _{n}=\frac{ n(t _{1}+ t _{n} )}{ 2 }\]
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
wait how does k =100 again?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
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)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
lower limit givs first term, upper limit gives last term
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
ok so 100 is the last term... And why do we multiply it by 5?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
last value of k is 100 general term = 5k so last term = 5*100
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
and the difference between the numbers would be five right? or is it something else
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yes, common difference = 2nd term 1st term = 3rd term 2nd term =.... = 105 = 1510 =.... = 5 but thats not required for the formula you are using
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
Oh ok that makes sense now. Maybe you should help me on other problems I post. Your a good help!
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
ok, sure, but did u get 25250 for this one ?
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
Oh wait quick question! What was \[t _{1}\] in this equation
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
t1 is the 1st term index represents which term
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
the index is which part again?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
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
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yup. as 5 is the 1st term
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
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
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
oh wait my bad! i got it
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
you mean in \(S_n = n (t_1+t_n)/2\) thats a general formula, do you want a derivation of this ?
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
What would happen when I solve for \[t _{n}\] in an equation where n did not equal 1 and it equaled something else?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
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
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
dw:1362289579021:dw Like this. N does not equal 1
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
i think u have made up this question ? or is it from your book/notes ?
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
here Ill give you one from the book. dw:1362289721775:dw
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
thats 30 m by the way. It kinda got cut off
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so, here your 1st term will start from m=10 in 30m and last term you'll get by putting m=20 in 30m
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
so how would i get \[t _{n}\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
tm = last term, last m =30 so to get last term tm, put m=30 in general term 30m is this confusing ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
general term tm =30m fist term t10 = 3010 (put m=10) last term t20 = 3020 (put m=20)
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
so I would do 30 10 first , and when do I do the 20? i dont know if that makes sense
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
ok lets not do this problem.. Ill ask my teacher on monday..
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
you have formula, you have n, you have 1st term, u have last term....just plug in values! ohh..ok, as u wish
 one year ago

sparky16Best ResponseYou've already chosen the best response.0
Ill be posting other problems so u may help me if u want
 one year ago
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