Question

Find the sum of the series.
[infinity] ln(1 − 1/n2) n = 2

Answer 1

The sum is -1/2

Explanation:

Your question is not too clear to me but if I reframe it, it will turn to this;

Find the sum of In{1 - (1/n^2)} for n >= 2

£n>=2 = In{1 - (1/2^2)} + In{1 - (1/3^2)} + In{1 - (1/4^2)} + ......

£n>=2 = In{1 - (1/4)} + In{1 - (1/9)} + In{1 - (1/16)}

£n>=2 = In(3/4) + In(8/9) + In(15/16)

£n>=2 = -0.287 + -0.117 + -.064 = −0.468

£n>=2 = -0.5 by approximation

£n>=2 = -1/2 is the sum and by evaluation it converge.