What is the sum from k=1 to infinity of sin(kpi) ?

The sum from k=1 to infinity of sin(kpi) is 0

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sum from k=1 to infinity of sin(kpi)

k = 1 \sum \infty sin (kπ)

0

Solution steps

k = 1 \sum \infty sin (kπ)

Use the basic trigonometric identity:

sin (nπ) = 0

= k = 1 \sum \infty 0

\sum 0 = 0

= 0

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What is the sum from k=1 to infinity of sin(kpi) ?
The sum from k=1 to infinity of sin(kpi) is 0