Write the sum using summation notation.
-$$\frac { 1 } { x + 3 } + \frac { 2 } { x + 6 } + \frac { 6 } { x + 9 } + \frac { 24 } { x + 12 } + \frac { 120 } { x + 15 }$$
A) $\sum _ { i = 1 } ^ { 5 } \frac { i ! } { x + 3 i }$
B) $\sum _ { i = 1 } ^ { 5 } \frac { i ! } { x + i }$
C) $\sum _ { i = 1 } ^ { 5 } \frac { 2 ^ { i - 1 } } { x + 3 i }$
D) $\sum _ { i = 1 } ^ { 5 } \frac { i ! } { x + 3 }$

Question

Quizplus · Accepted Answer

The terms in the series can be represented by $\frac{i!}{x + 3i}$, where $i!$ denotes the factorial of $i$ (e.g., $1!, 2!, 6!, 24!, 120!$), and the denominator increases by 3 for each term ($x+3, x+6, x+9, \ldots$). This matches the pattern described in option A.

Write the Sum Using Summation Notation 1x+3+2x+6+6x+9+24x+12+120x+15\frac { 1 } { x + 3 } + \frac { 2 } { x + 6 } + \frac { 6 } { x + 9 } + \frac { 24 } { x + 12 } + \frac { 120 } { x + 15 }x+31​+x+62​+x+96​+x+1224​+x+15120​

Write the Sum Using Summation Notation $\frac { 1 } { x + 3 } + \frac { 2 } { x + 6 } + \frac { 6 } { x + 9 } + \frac { 24 } { x + 12 } + \frac { 120 } { x + 15 }$