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Series Question 2 watch

1. find the sum of 2n terms of the series

$1^{2}-3^{2}+5^{2}-7^{2}+...$
2. That looks like an expression rather than a series?
3. (Original post by BobBobson)
That looks like an expression rather than a series?
It says series im just copying what the question says
4. (Original post by Carman3)
find the sum of 2n terms of the series

$1^{2}-3^{2}+5^{2}-7^{2}+...$
Generalise the series in terms of n and do the sum from 1 to 2n.
To generalise , you're going to have to multiply by (-1)^f(n) so the signs oscillate.
5. (Original post by Carman3)
find the sum of 2n terms of the series

$1^{2}-3^{2}+5^{2}-7^{2}+...$
Write an expression for S(2n) in terms of a summation over i=1..n of two terms. You can then expand and simplify the expression. The result falls-out quite nicely.
6. (Original post by NotNotBatman)
Generalise the series in terms of n and do the sum from 1 to 2n.
To generalise , you're going to have to multiply by (-1)^f(n) so the signs oscillate.
(Original post by RogerOxon)
Write an expression for S(2n) in terms of a summation over i=1..n of two terms. You can then expand and simplify the expression. The result falls-out quite nicely.
Can you show me how its done?
7. (Original post by Carman3)
Can you show me how its done?
Here's a start:

Edit: Which is wrong .. I should be using 4i as the base and adding
8. Dont know how to go further from there

(Original post by RogerOxon)
Here's a start:
9. (Original post by Carman3)
Dont know how to go further from there
Expand the squared terms and simplify.
10. (Original post by RogerOxon)
Expand the squared terms and simplify.
Ok i managed to get
−8n^2 which was the right answer.. But now part b) says hence find the sum of 2n+1 terms which i dont know how to do
11. (Original post by Carman3)
Ok i managed to get
−8n^2 which was the right answer.. But now part b) says hence find the sum of 2n+1 terms which i dont know how to do
You already have the sum to 2n terms, so add the additional one.
12. (Original post by RogerOxon)
You already have the sum to 2n terms, so add the additional one.
So what would the answer be?

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