Rewrite the series using summation notation. Use 1 as the lower limit of summation.
-$$\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }$$
A) $\sum _ { i = 1 } ^ { 14 } \frac { i - 2 } { i }$
B) $\sum _ { i = 1 } ^ { 14 } \frac { i } { i + 2 }$
C) $\sum _ { i = 2 } ^ { 14 } \frac { i } { i + 1 }$
D) $\sum _ { i = 0 } ^ { 14 } \frac { i } { i + 2 }$

Question

Quizplus · Accepted Answer

The given series starts with $\frac{1}{3}$, which can be represented as $\frac{1}{1+2}$, and ends with $\frac{7}{8}$, which is $\frac{6}{6+2}$. This pattern suggests that the numerator starts at 1 and increases by 1 with each term, while the denominator is always 2 more than the numerator. Option B, $\sum _ { i = 1 } ^ { 14 } \frac { i } { i + 2 }$, correctly represents this pattern, starting from 1 and going up to 14 to include all terms of the series.

Rewrite the Series Using Summation Notation 13+12+35+…+78\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }31​+21​+53​+…+87​

Rewrite the Series Using Summation Notation $\frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 3 } { 5 } + \ldots + \frac { 7 } { 8 }$