What is the sum from n=0 to infinity of 7/(10^{-n)} ?

The sum from n=0 to infinity of 7/(10^{-n)} is diverges

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sum from n=0 to infinity of 7/(10^{-n)}

n = 0 \sum \infty \frac{7}{1 0 ^{- n}}

diverges

Solution steps

n = 0 \sum \infty \frac{7}{1 0 ^{- n}}

Apply the constant multiplication rule:

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

= 7 \cdot n = 0 \sum \infty \frac{1}{1 0 ^{- n}}

Simplify

\frac{1}{1 0 ^{- n}} : 1 0^{n}

= 7 \cdot n = 0 \sum \infty 1 0^{n}

Apply Series Geometric Test:

diverges

= 7 diverges

= diverges

n = 1 \sum \infty \frac{4}{4 ^{n} + 1}

n = 1 \sum \infty \frac{2}{3 n}

n = 1 \sum \infty \frac{2 n}{7 n - 4}

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

n = 1 \sum \infty \frac{n ^{2}}{n ^{4}}

What is the sum from n=0 to infinity of 7/(10^{-n)} ?
The sum from n=0 to infinity of 7/(10^{-n)} is diverges