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**Blizzardy** Hi guys, please help with this QNS:

By considering 1/(1 + a^n-1) - 1/(1 + a^n), deduce Σ (a^n)/[(1 + a^n-1)(1 + a^n)] upper limit: N, lower limit: n = 1

So this is how I did it:

1/(1 + a^n-1) - 1/(1 + a^n) = a^n/[(1 + a^n-1)(1 + a^n)]** -** a^n-1/[(1 + a^n-1)(1 + a^n)]

(a^n)/[(1 + a^n-1)(1 + a^n)] = 1/(1 + a^n-1) - 1/(1 + a^n) **+** a^n-1/[(1 + a^n-1)(1 + a^n)]

=> Σ (a^n)/[(1 + a^n-1)(1 + a^n)] = Σ (1/(1 + a^n-1) - 1/(1 + a^n) **+** a^n-1/[(1 + a^n-1)(1 + a^n)] )

(Then I use the method of difference by substituting n = 1,2,3.. but I couldn't solve since there isn't a standard way of cancelling the terms)