What is the sum from n=0 to infinity of 5(9/10)^n ?

The sum from n=0 to infinity of 5(9/10)^n is 50

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sum from n=0 to infinity of 5(9/10)^n

n = 0 \sum \infty 5 (\frac{9}{10})^{n}

50

Solution steps

n = 0 \sum \infty 5 (\frac{9}{10})^{n}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 5 \cdot n = 0 \sum \infty (\frac{9}{10})^{n}

Apply Series Geometric Test:

10

= 5 \cdot 10

Simplify

= 50

n = 0 \sum \infty (\frac{3}{n})^{\frac{1}{n}}

n = 2 \sum \infty \frac{n ^{4}}{n ^{3}}

n = 2 \sum \infty n e^{- 5 n}

n = 0 \sum \infty e^{3 n}

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

What is the sum from n=0 to infinity of 5(9/10)^n ?
The sum from n=0 to infinity of 5(9/10)^n is 50