Express the sum using summation notation. -$$\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$$ A) $\sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } } } { \mathrm { kw } }$ B) $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$ C) $\sum _ { k = 0 } ^ { n } \frac { k } { k w }$ D) $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } - 1 } } { \mathrm { kw } }$

Question

Express the sum using summation notation.
-$$\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$$
A) $\sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } } } { \mathrm { kw } }$

B) $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$

C) $\sum _ { k = 0 } ^ { n } \frac { < b > k } { k w }$

D) $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \frac { \mathrm { s } ^ { \mathrm { k } - 1 } } { \mathrm { kw } }$

Quizplus · Accepted Answer

The given series starts with $s^0$ (which is 1) in the numerator and the denominator starts with 1. The index k needs to start at 1 to match the first term and increment by 1 for each term, with the power of s being one less than k (hence $s^{k-1}$). The denominator matches the pattern $kw$, making option B the correct representation using summation notation.

Express the Sum Using Summation Notation 1w+s2w+s23w+…+sn−1nw\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }w1​+2ws​+3ws2​+…+nwsn−1​

Express the Sum Using Summation Notation $\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$