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# P4 Summation of Series watch

1. Having partial-fractioned 1/(r^2 - 1) into 0.5/(r-1) - 0.5/(r+1), could someone please explain how I would then go about summing the series for r=2 to n?
2. You can use the difference method.

You have already got 1/(2(r-1)) - 1/(2(r+1))

so when r=n you have: 1/(2(n-1)) - 1/(2(n+1))

and when r= n-1 : 1/(2(n-2)) - 1/(2(n))

and when r= n-2 : 1/(2(n-3)) - 1/(2(n-1))

and this would continue to

when r=4 1/6 - 1/10

when r=3 1/4 - 1/8

when r=2 1/2 - 1/6

(NOTE: its from 2 to n so theres no r=1)

Now if you look at these terms they will all cancel excludingthe first terms of r=2 and r=3 and the last terms of r=n and r=n-1.

Therefore you are left with

3/4 - 1/(2n) - 1/(2(n+1))

which i think is the right answer. Hope this helps.
3. (Original post by SUKBarracuda)

Hope this helps.
It certainly does! Thankyou very much.

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