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

Question

Quizplus · Accepted Answer

We can see that each term is alternately positive and negative, so we can use the alternating property of summation to write the sum in sigma notation as:
$$\sum _ { k = 1 } ^ { 5 } ( - 1 ) ^ { k } \frac { k } { 5 }$$
Since the signs alternate starting with the first term being negative, we use the power of k instead of k-1 or k+1 in the exponent of -1. Therefore, the correct choice is D.

Express the Sum in Sigma Notation −15+25−35+45−55- \frac { 1 } { 5 } + \frac { 2 } { 5 } - \frac { 3 } { 5 } + \frac { 4 } { 5 } - \frac { 5 } { 5 }−51​+52​−53​+54​−55​

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