Write the sum using summation notation.
-$$\frac { 1 } { 5 } + \frac { 4 } { 3 } + \frac { 27 } { 7 } + \ldots + \frac { n ^ { 3 } } { n + 4 }$$
A) $\sum _ { i = 0 } ^ { n } \frac { i ^ { 3 } } { i + 4 }$
B) $\sum _ { i = 1 } ^ { n } \frac { n ^ { 3 } } { n + 4 }$
C) $\sum _ { i = 1 } ^ { n + 1 } \frac { i ^ { 3 } } { i + 4 }$
D) $\sum _ { i = 1 } ^ { n } \frac { i ^ { 3 } } { i + 4 }$

Question

Quizplus · Accepted Answer

The given series starts with the term $\frac{1^3}{1+4}$ and ends with the term $\frac{n^3}{n+4}$, indicating that the index $i$ starts at 1 and ends at $n$. The general term of the series is $\frac{i^3}{i+4}$, which matches option D.

Write the Sum Using Summation Notation 15+43+277+…+n3n+4\frac { 1 } { 5 } + \frac { 4 } { 3 } + \frac { 27 } { 7 } + \ldots + \frac { n ^ { 3 } } { n + 4 }51​+34​+727​+…+n+4n3​

Write the Sum Using Summation Notation $\frac { 1 } { 5 } + \frac { 4 } { 3 } + \frac { 27 } { 7 } + \ldots + \frac { n ^ { 3 } } { n + 4 }$