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

Question

Quizplus · Accepted Answer

The given sequence can be represented by the formula $\frac{i}{i+2}$, starting with $i=1$ to generate $\frac{1}{3}$, and continuing in this pattern. The last term, $\frac{7}{8}$, corresponds to $i=6$, since $\frac{6}{6+2} = \frac{6}{8} = \frac{3}{4}$, indicating a mistake in identifying the last term. However, based on the pattern and options provided, option A correctly represents the sequence with the formula $\frac{i}{i+2}$ starting from $i=1$, but the sequence description or the last term as given seems to have an inconsistency with the options provided. Option A is the closest match to the pattern described, assuming there might be a typographical error in the description of the last term of the sequence.

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

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