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# FP1 Sigma Notation watch

1. Find the sum of n terms of the series:
(p-1)(p+1) + (p-2)(p+2)...

I assume its something to do with alternating sign sequences (-1)^r and (-1)^r+1, but I'm not entirely sure where to start.
2. (Original post by olegasr)
Find the sum of n terms of the series:
(p-1)(p+1) + (p-2)(p+2)...

I assume its something to do with alternating sign sequences (-1)^r and (-1)^r+1, but I'm not entirely sure where to start.
I'd start by multiplying out each pair of brackets - it's not as bad as it looks.

I presume "p" is an unknown, and the terms go to (p+n)(p-n). If not, please clarify.
3. (Original post by ghostwalker)
I'd start by multiplying out each pair of brackets - it's not as bad as it looks.

I presume "p" is an unknown, and the terms go to (p+n)(p-n). If not, please clarify.
That's correct. Multiplying out brackets allows you to establish the pattern of (p^2 - n^2). I'm not entirely sure what to do next with this information.
The answer at the end of the book is np^2 - 1/6n(n+1)(2n+1).
4. (Original post by olegasr)
That's correct. Multiplying out brackets allows you to establish the pattern of (p^2 - n^2). I'm not entirely sure what to do next with this information.
The answer at the end of the book is np^2 - 1/6n(n+1)(2n+1).
Well you're summing this for n terms, so rearranging the sum you have:

(p^2 + p^2+...(n times in all )... + p^2) - (1^2 +2^2+... +n^2)

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