SOLUTION: Evaluate: ∞ Σ (1/3)(-4/3)^k k=1 I hope I asked this right, the infinite is on top of the sigma. K=1 is on the bottom. And the rest is to the right of the sigma

Algebra ->  Sequences-and-series -> SOLUTION: Evaluate: ∞ Σ (1/3)(-4/3)^k k=1 I hope I asked this right, the infinite is on top of the sigma. K=1 is on the bottom. And the rest is to the right of the sigma      Log On


   

Question 1040821: Evaluate:
∞
Σ (1/3)(-4/3)^k
k=1
I hope I asked this right, the infinite is on top of the sigma. K=1 is on the bottom. And the rest is to the right of the sigma. Thank you! Just want to check my answer, haven't done sequences since high school.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

This is a geometric series of the form a%2Ar%5En where n is a whole number.

In this case, a+=+1%2F3 and r+=+-4%2F3

The rule is this: an infinite geometric series converges to a fixed number if and only if -1+%3C+r+%3C+1

But because r+=+-4%2F3+=+-1.33 (approx) is NOT in the interval -1+%3C+r+%3C+1, this means that the infinite geometric series does NOT converge.

So the geometric series diverges. It will not approach a fixed number>