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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
12. (Original post by RogerOxon)
So what would the answer be?

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