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**simple limit?**

## Homework Statement

I am trying to prove if a series is convergent.

the series is a(sub n) = (2/3)[2^n - 2^(-n)] from n=1 to infinity.

## Homework Equations

Ratio test:

the limit as n approached infinity of the absolute value of a(sub n+1) /a(sub n) equals r.

If r is less than one the series converges.

if r is greater than 1 the series diverges.

## The Attempt at a Solution

lim as n approaches infinity of the absolute value of

__(2/3 * (2^(n+1) - 2 ^(-n+1)))__

(2/3 * (2^n - 2^(-n)))

eqauls r

the 2/3 cancel and I get

lim as n approaches infinity of the absolute value of

__(2^(n+1) - 2 ^(-n+1))__

(2^n - 2^(-n))

eqauls r

this is where I get stuck. Looking at the graph of this function, I can see that the limit is 2. But I don't know how to show it. It has been a long time since I took Calc...

PLEASE HELP