- #1

- 90

- 0

## Homework Statement

So, I actually have a bunch of these problems and I cannot do any of them. I don't think I'm really understanding it. Here is the question: (one of them) The way I wrote them, a_n means a sub n

For each sequence a_n find a number k such that n^k a_n

has a finite non-zero limit.

(This is of use, because by the limit comparison test the series ∑from 1 to infinity (a_n) and ∑from 1 to infinity (n^-k) both converge or both diverge.)

The question:

a_n= (6+3n)^-7

What does k equal?

## Homework Equations

N/A

## The Attempt at a Solution

I'm actually 100% lost on this problem. I don't even know where to start :(

Here's my attempt. It may not make any sense because I don't understand this. But here it is:

(6+3n)^-7>0

1/(6+3n)^7>0

1>0

Ans: 1

But that is incorrect.