Write the series using summation notation.
-$$1 ^ { 8 } + 2 ^ { 8 } + 3 ^ { 8 } + 4 ^ { 8 } + \ldots$$
A) $\sum _ { \mathrm { k } = 1 } ^ { \infty } \mathrm { k } ^ { 7 }$

B) $\sum _ { \mathrm { k } = 1 } ^ { 4 } \mathrm { k } ^ { 8 }$

C) $\sum _ { k = 1 } ^ { \infty } \mathrm { k } ^ { 8 }$

D) $\sum _ { \mathrm { k } = 0 } ^ { \infty } 8 ^ { \mathrm { k } }$

Question

Write the series using summation notation.
-$$1 ^ { 8 } + 2 ^ { 8 } + 3 ^ { 8 } + 4 ^ { 8 } + \ldots$$
A) $\sum _ { \mathrm { k } = 1 } ^ { \infty } \mathrm { k } ^ { 7 }$

B) $\sum _ { \mathrm { k } = 1 } ^ { 4 } \mathrm { k } ^ { 8 }$

C) $\sum _ { k = 1 } ^ { \infty } \mathrm { k } ^ { 8 }$

D) $\sum _ { \mathrm { k } = 0 } ^ { \infty } 8 ^ { \mathrm { k } }$

Quizplus · Accepted Answer

The series $1^8 + 2^8 + 3^8 + 4^8 + \ldots$ represents the sum of $k^8$ for each integer $k$ starting from 1 and continuing indefinitely. The correct summation notation for this series is $\sum _ { k = 1 } ^ { \infty } k ^ { 8 }$, which matches option C.

Write the Series Using Summation Notation 18+28+38+48+…1 ^ { 8 } + 2 ^ { 8 } + 3 ^ { 8 } + 4 ^ { 8 } + \ldots18+28+38+48+…

Write the Series Using Summation Notation $1 ^ { 8 } + 2 ^ { 8 } + 3 ^ { 8 } + 4 ^ { 8 } + \ldots$