What is the sum from n=0 to infinity of cos(5n)pi ?

The sum from n=0 to infinity of cos(5n)pi is diverges

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sum from n=0 to infinity of cos(5n)pi

n = 0 \sum \infty cos (5 n) π

diverges

Solution steps

n = 0 \sum \infty cos (5 n) π

Apply the constant multiplication rule:

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

= π \cdot n = 0 \sum \infty cos (5 n)

Apply Series Divergence Test:

diverges

= π diverges

= diverges

x = 0 \sum \infty ln (x)

n = 0 \sum \infty \frac{1}{n + 17}

k = 2 \sum \infty \frac{4}{7 ^{k}}

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

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

What is the sum from n=0 to infinity of cos(5n)pi ?
The sum from n=0 to infinity of cos(5n)pi is diverges