What is the sum from n=0 to infinity}2^{-n of+3^{-n} ?

The sum from n=0 to infinity}2^{-n of+3^{-n} is 7/2

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sum from n=0 to infinity}2^{-n of+3^{-n}

n = 0 \sum \infty 2^{- n} + 3^{- n}

\frac{7}{2}

Solution steps

n = 0 \sum \infty 2^{- n} + 3^{- n}

Apply the Sum Rule:

\sum a_{n} + b_{n} = \sum a_{n} + \sum b_{n}

= n = 0 \sum \infty 2^{- n} + n = 0 \sum \infty 3^{- n}

n = 0 \sum \infty 2^{- n} = 2

n = 0 \sum \infty 3^{- n} = \frac{3}{2}

= 2 + \frac{3}{2}

Simplify

2 + \frac{3}{2} : \frac{7}{2}

= \frac{7}{2}

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What is the sum from n=0 to infinity}2^{-n of+3^{-n} ?
The sum from n=0 to infinity}2^{-n of+3^{-n} is 7/2