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**oblixps** find a closed form for the nth partial sum of the series and determine whether the series converges. If so, find its sum.

ln(1 - (1/4)) + ln(1 - (1/9)) + ln(1 - (1/16)) +...+ ln(1 - (1/(k+1)^2)+...

using log properties i got the first few partial sums as S1 = 3/4, S2 = 2/3, S3 = 5/8, S4 = 3/5 but i can't seem to find a pattern. also in the answers in the back of the book, even though this question asked for a closed form, the back of the book gave: sum from k=2 to (n+1) of [ln((k-1)/(k)) - ln(k/(k+1))]. i thought closed form meant without a summation symbol. i am confused.