Express the sum in sigma notation.
-$$\frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } + \frac { 1 } { 16 }$$
A) $\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( \frac { 1 } { 2 } \right) ^ { \mathrm { k } - 1 }$
B) $\sum _ { \mathrm { k } = 0 } ^ { 4 } \left( \frac { 1 } { 2 } \right) ^ { \mathrm { k } + 1 }$
C) $\sum _ { k = 1 } ^ { 4 } \left( \frac { 1 } { 2 } \right) ^ { k }$
D) $\sum _ { k = 1 } ^ { 5 } \left( \frac { 1 } { 2 } \right) ^ { k - 1 }$

Question

Quizplus · Accepted Answer

The given series consists of four terms each of which is half the value of the previous term. Therefore, the sum can be written as
$$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=\sum_{k=1}^{4}\left(\frac{1}{2}\right)^k$$
Thus, the correct choice is $\boxed{\textbf{(C)}}$.

Express the Sum in Sigma Notation 12+14+18+116\frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } + \frac { 1 } { 16 }21​+41​+81​+161​

Express the Sum in Sigma Notation $\frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } + \frac { 1 } { 16 }$