Write the series using summation notation.
-$$\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }$$
A) $\sum _ { i = 1 } ^ { 5 } \frac { i } { i ( i + 1 ) }$

B) $\sum _ { i = 1 } ^ { 5 } \frac { i + 2 } { i ( i - 1 ) }$

C) $\sum _ { i = 1 } ^ { 5 } \frac { i + 2 } { i ( i + 1 ) }$

D) $\sum _ { i = 1 } ^ { 5 } \frac { i - 2 } { i ( i + 1 ) }$

Question

Write the series using summation notation.
-$$\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }$$
A) $\sum _ { i = 1 } ^ { 5 } \frac { i } { i ( i + 1 ) }$

B) $\sum _ { i = 1 } ^ { 5 } \frac { i + 2 } { i ( i - 1 ) }$

C) $\sum _ { i = 1 } ^ { 5 } \frac { i + 2 } { i ( i + 1 ) }$

D) $\sum _ { i = 1 } ^ { 5 } \frac { i - 2 } { i ( i + 1 ) }$

Quizplus · Accepted Answer

Each term of the series can be represented as $\frac{i+2}{i(i+1)}$ where $i$ starts from 1 and goes up to 5, matching the pattern of the given series.

Write the Series Using Summation Notation 31⋅2+42⋅3+53⋅4+64⋅5+75⋅6\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }1⋅23​+2⋅34​+3⋅45​+4⋅56​+5⋅67​

Write the Series Using Summation Notation $\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }$