Write the sum without sigma notation and evaluate it.
-$$\sum _ { \mathrm { k } = 1 } ^ { 3 } 5 ^ { \mathrm { k } } \sin \frac { \pi } { 6 }$$
A) $5 \sin \frac { \pi } { 6 } + 125 \sin \frac { \pi } { 6 } = 65$
B) $5 + 25 + 125 = 155$
C) $5 \sin \frac { \pi } { 6 } + 25 \sin \frac { \pi } { 6 } + 125 \sin \frac { \pi } { 6 } = \frac { 155 } { 2 }$
D) $5 \sin \frac { \pi } { 6 } + 25 \sin \frac { \pi } { 6 } + 125 \sin \frac { \pi } { 6 } = \frac { 155 } { 2 } \sqrt { 3 }$

Question

Quizplus · Accepted Answer

We can simply calculate each term and add them up:

\begin{align*}
\sum_{k=1}^3 5^k\sin\frac{\pi}{6} &= 5\sin\frac{\pi}{6}+5^2\sin\frac{\pi}{6}+5^3\sin\frac{\pi}{6} \
&= 5\cdot\frac{1}{2}+25\cdot\frac{1}{2}+125\cdot\frac{1}{2} \
&= \frac{155}{2}
\end{align*}

Therefore, the correct choice is C.

Write the Sum Without Sigma Notation and Evaluate It ∑k=135ksin⁡π6\sum _ { \mathrm { k } = 1 } ^ { 3 } 5 ^ { \mathrm { k } } \sin \frac { \pi } { 6 }k=1∑3​5ksin6π​

Write the Sum Without Sigma Notation and Evaluate It $\sum _ { \mathrm { k } = 1 } ^ { 3 } 5 ^ { \mathrm { k } } \sin \frac { \pi } { 6 }$