Hello All! Two series questions from my homework that I didn't know how to do:
Objective: Test for Convergence or Divergence
1) Sum (n=1 to Infinity) of 3n+2/(n(n+1))
3n+2/(n^2+n). Since it's decreasing I can apply the Integral test, correct? I could split it into 3n/(n^2+n) = 3/n+1 (easy to integrate) and 2/(n^2 +n). I don't know how to integrate this second part -- unless you can do it by partial fractions with A/(x) + B/(x+1). That might work actually. Is this correct?
2) Sum (n = 2 to Infinity) of 1/(n*(ln(n)^2). With the integral test (f(x) = 1/(x*(ln(x)^2), I could set u = ln(x), and du = 1/x, to get lim (t->Infinity) of Integral u^2du, but the bounds would be strange right? They would be ln(2) and ln(t). I could carry on this way but is this correct? I hate setting up a problem incorrectly and then having to work all the way through it!
Thanks once again: this forum is fantastic!!!!