Question

Integral and Comparison Problem

Answer 1

The first part seems to be convergent by the geometric series?

Answer 2

compare to 1/3^n = n/n*3^3>n/(n+1)*3^n for the first

Answer 3

Yes so the first one is convergent.

Answer 4

the second also converges. compare to n/n^3 > n/n^3-2n+6 for n > 3

Answer 5

Could I compare the second one with 1/n^2?

Answer 6

Alrighty, how would I do the last one?

Answer 7

i think the integral test. do a u sub with u = ln(n) and then do another u sub (actually do a t sub) with t = ln u and see what you get

Answer 8

i think it's still gonna diverge but you'll have to check

Answer 9

Okay thank you!

Answer 10

you're welcome