Find the sum of the sequence.
-$$\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { \mathrm { k } }$$
A) $\frac { 5 } { 16 }$
B) $\frac { 15 } { 16 }$
C) $- \frac { 1 } { 16 }$
D) $- \frac { 5 } { 16 }$

Question

Quizplus · Accepted Answer

The sum of the sequence is calculated by plugging in the values of $k$ from 1 to 4 into the given formula and adding the results: $$ \sum _ { k = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { k } = \left( - \frac { 1 } { 2 } \right) ^ { 1 } + \left( - \frac { 1 } { 2 } \right) ^ { 2 } + \left( - \frac { 1 } { 2 } \right) ^ { 3 } + \left( - \frac { 1 } { 2 } \right) ^ { 4 } = -\frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} = -\frac{5}{16}.$$

Find the Sum of the Sequence ∑k=14(−12)k\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { \mathrm { k } }k=1∑4​(−21​)k

Find the Sum of the Sequence $\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( - \frac { 1 } { 2 } \right) ^ { \mathrm { k } }$