What is the sum from k=1 to infinity of (-1)^k ?

The sum from k=1 to infinity of (-1)^k is diverges

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sum from k=1 to infinity of (-1)^k

k = 1 \sum \infty (- 1)^{k}

diverges

Solution steps

k = 1 \sum \infty (- 1)^{k}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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\int \frac{13}{( x - 2 ) ( x ^{2} + 9 )} d x

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