What is the sum from n=0 to infinity of-1^{2n} ?

The sum from n=0 to infinity of-1^{2n} is diverges

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sum from n=0 to infinity of-1^{2n}

n = 0 \sum \infty - 1^{2 n}

diverges

Solution steps

n = 0 \sum \infty - 1^{2 n}

Apply the constant multiplication rule:

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

= - n = 0 \sum \infty 1^{2 n}

Simplify

= - n = 0 \sum \infty 1

Every infinite sum of a non-zero constant diverges

= - diverges

= diverges

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What is the sum from n=0 to infinity of-1^{2n} ?
The sum from n=0 to infinity of-1^{2n} is diverges