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

Question

Quizplus · Accepted Answer

The numerator of each fraction increases by 1 starting from 3, and the denominator is the product of consecutive numbers starting from 1. Option A correctly represents this pattern with $i+2$ in the numerator and $i(i+1)$ in the denominator.

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 $\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }$