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) $\sum _ { k = 1 } ^ { n } \frac { s ^ { k } } { k w }$ B) $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$ C) $\sum _ { k = 0 } ^ { n } \frac { k } { k w }$ D) $\sum _ { k = 0 } ^ { n } \frac { s ^ { k - 1 } } { k w }$

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) $\sum _ { k = 1 } ^ { n } \frac { s ^ { k } } { k w }$
B) $\sum _ { k = 1 } ^ { n } \frac { s ^ { k - 1 } } { k w }$
C) $\sum _ { k = 0 } ^ { n } \frac { < b > k } { k w }$
D) $\sum _ { k = 0 } ^ { n } \frac { s ^ { k - 1 } } { k w }$

Quizplus · Accepted Answer

The given series starts with $s^0$ (which is 1) in the numerator and the denominator starts with 1. The index $k$ in the correct summation notation should start at 1 and go up to $n$, with the numerator being $s^{k-1}$ to correctly represent the sequence starting from $s^0$. The denominator correctly increases by 1 with each term, starting from 1, and includes $w$ as a factor.

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 $\frac { 1 } { w } + \frac { s } { 2 w } + \frac { s ^ { 2 } } { 3 w } + \ldots + \frac { s ^ { n - 1 } } { n w }$