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

The sum from n=0 to infinity of sin(pi*n) is 0

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sum from n=0 to infinity of sin(pi*n)

n = 0 \sum \infty sin (π \cdot n)

0

Solution steps

n = 0 \sum \infty sin (πn)

Use the basic trigonometric identity:

sin (nπ) = 0

= n = 0 \sum \infty 0

\sum 0 = 0

= 0

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