Calculus question involving an infinite series

[christophermu]

The series from n = 1 infinity of 1/(n*(3^n)) must

A) converge to a value greater than 1/4
B) converge to a value greater than 1/9
C) Converge to a value less than 1/8
D) converge to a value less than 1/2
E) diverge.

I know the series definitely does not diverge because the series (1/3)^n is a geometric series which converges and the series is question is smaller than that geometric series so it much converge by the direct comparision test.

But I am not sure how to see what it would converge to. Can someone help?

 

[rs1n]

The series from n = 1 infinity of 1/(n*(3^n)) must

A) converge to a value greater than 1/4
B) converge to a value greater than 1/9
C) Converge to a value less than 1/8
D) converge to a value less than 1/2
E) diverge.

I know the series definitely does not diverge because the series (1/3)^n is a geometric series which converges and the series is question is smaller than that geometric series so it much converge by the direct comparision test.

But I am not sure how to see what it would converge to. Can someone help?

Given the multiple choices, just look at the first term in your infinite series. What can you conclude?

 

[lanedance]

so you've ruled out E)

couple of things to consider...
- what does 1/3^n converge to? then what can you say about each term of your series relative to that series

- what do the first few terms add upto, can you rule out any other answers?

 

[lanedance]

welcome to PF by the way