Answer
$0$
Work Step by Step
Substitute $1,2,3,4,5$ to $k$ and calculate the sum:
$$\begin{align*}
\displaystyle\Sigma_{k=1}^5 \sin k\pi &\\
&=\sin \pi+\sin 2\pi+\sin 3\pi+\sin 4\pi+\sin 5\pi \\
&=0+0+0+0+0\\
&=0.
\end{align*}$$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 5: Integrals - Section 5.2 - Sigma Notation and Limits of Finite Sums - Exercises 5.2 - Page 265: 4
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