Express the sum in sigma notation.
-$$- \frac { 1 } { 7 } + \frac { 2 } { 7 } - \frac { 3 } { 7 } + \frac { 4 } { 7 } - \frac { 5 } { 7 }$$
A) $\sum _ { \mathrm { k } = 1 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } + 1 } \frac { \mathrm { k } } { 7 }$
B) $\sum _ { \mathrm { k } = 1 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } } \frac { \mathrm { k } } { 7 }$
C) $\sum _ { \mathrm { k } = 0 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } - 1 } \frac { \mathrm { k } } { 7 }$
D) $\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } \frac { k + 1 } { 7 }$

Question

Quizplus · Accepted Answer

The given sum consists of alternating signs and a linear function of k. Therefore, we can use sigma notation with (-1)^(k) as the alternating sign and k/7 as the linear function. Since k starts at 1 and goes up to 5, the correct sigma notation is:  $\sum_{k=1}^5 (-1)^{k}\frac{k}{7}$. This matches with Choice B.

Express the Sum in Sigma Notation −17+27−37+47−57- \frac { 1 } { 7 } + \frac { 2 } { 7 } - \frac { 3 } { 7 } + \frac { 4 } { 7 } - \frac { 5 } { 7 }−71​+72​−73​+74​−75​

Express the Sum in Sigma Notation $- \frac { 1 } { 7 } + \frac { 2 } { 7 } - \frac { 3 } { 7 } + \frac { 4 } { 7 } - \frac { 5 } { 7 }$