What is the sum from n=1 to infinity of (-1)^{2n+1} ?

The sum from n=1 to infinity of (-1)^{2n+1} is diverges

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sum from n=1 to infinity of (-1)^{2n+1}

n = 1 \sum \infty (- 1)^{2 n + 1}

diverges

Solution steps

n = 1 \sum \infty (- 1)^{2 n + 1}

Apply Series Divergence Test

= diverges

n = 1 \sum \infty (\frac{1}{5})^{n} + \frac{3}{n}

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

m = 1 \sum \infty \frac{5}{m ln ( 3 m )}

n = 1 \sum \infty \frac{5}{4 ^{n} + 1}

n = 0 \sum \infty \frac{1}{6 ^{n} - 5}

What is the sum from n=1 to infinity of (-1)^{2n+1} ?
The sum from n=1 to infinity of (-1)^{2n+1} is diverges