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First, determine if the series converges.

SUM: (n-2)/(n^2-4n) (from n=5 to infinity)

I used the integral test, found the integral to be 1/2 log(n^2-4n) from x=5 to x=t as t approaches infinity. That turned out to go to infinity so the series diverges.

Does this seem right or did I do something wrong?

Second, Suppose a series is the SUM: (1 - ((2^(k-1) - 1) / (2^(k+1)))

Does the sum of the series converge or diverge? I'm not really even sure where to start this one.