What is the sum from n=0 to infinity of cos(n)pi ?

The sum from n=0 to infinity of cos(n)pi is diverges

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sum from n=0 to infinity of cos(n)pi

n = 0 \sum \infty cos (n) π

diverges

Solution steps

n = 0 \sum \infty cos (n) π

Apply the constant multiplication rule:

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

= π \cdot n = 0 \sum \infty cos (n)

Apply Series Divergence Test:

diverges

= π diverges

= diverges

n = 1 \sum \infty \frac{1}{3 ^{n} n !}

n = 1 \sum \infty (\frac{2}{n})^{3}

n = 1 \sum \infty cos (\frac{3}{n})

n = 0 \sum \infty (\frac{1}{π})^{n}

n = 0 \sum \infty 2 (\frac{3}{4})^{n}

What is the sum from n=0 to infinity of cos(n)pi ?
The sum from n=0 to infinity of cos(n)pi is diverges