Question

Determine whether the series is convergent or divergent. If it is convergent, find its sum.

Answer 1

\[\sum_{n=1}^{\infty} (1+3^n)/2^n\]

Answer 2

no chance

Answer 3

1/2^n + (3/2)^n

Answer 4

(3/2)^n should be a tip-off...

Answer 5

\[\frac{1+3^n}{2^n}>\frac{3^n}{n^n}\] terns don't even go to zero

Answer 6

So what does that mean?

Answer 7

typo there, but you get the idea
\[\frac{1+3^n}{2^n}>\frac{3^n}{2^n}\] *terms don't go to zero

Answer 8

a necessary (but not sufficient) condition for the sum to converge is that the terms go to zero

Answer 9

it's a geometric series with |r| >1

Answer 10

Okay, thanks.