What is the sum from n=0 to infinity of (-1)^n5^n ?

The sum from n=0 to infinity of (-1)^n5^n is diverges

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sum from n=0 to infinity of (-1)^n5^n

n = 0 \sum \infty (- 1)^{n} 5^{n}

diverges

Solution steps

n = 0 \sum \infty (- 1)^{n} \cdot 5^{n}

Apply Series Ratio Test:

diverges

= diverges

n = 1 \sum \infty \frac{1}{6 n + 1}

n = 0 \sum \infty (\frac{8 π}{e})^{n}

n = 1 \sum \infty (cos (20))^{n}

x = 1 \sum \infty \frac{x}{e ^{x}}

k = 0 \sum \infty (\frac{5}{6})^{k}

What is the sum from n=0 to infinity of (-1)^n5^n ?
The sum from n=0 to infinity of (-1)^n5^n is diverges