Question

Find the value of the series (2^n+1)/3^n.

Answer 1

From n=1 to infinity.

Answer 2

@dumbcow @iambatman

Answer 3

@myininaya @RadEn

Answer 4

is it
A) \((2^n+1)/3^n\)
or
B) \(2^{n+1}/3^n\) ?

Answer 5

B.

Answer 6

ok.
When seeing these powers, you might thnk about the geometric formula
\[\sum_{n=0}^\infty x^n = \frac{1}{1-x}\quad\text{if } 0<x<1.
\]
and try to make your series look like that (factor out a few things).

Answer 7

So you mean that this is geometric series?

Answer 8

\[\frac{2^{n+1}}{3^n} = 2 (\frac{2}{3})^n\]

Answer 9

Got it. Thank you so much, dumbcow.