Chapter 11.4, Problem 11WE

To determine

To calculate:

Given series using sigma notation.

Answer to Problem 11WE

Given series $1^3+2^3+3^3+\mathrm{...}+{20}^3$ using sigma notation is ${\displaystyle \sum _{n=0}^{20}{\left(n+1\right)}^3}$ .

Explanation of Solution

Give information:

Expression:

  $1^3+2^3+3^3+\mathrm{...}+{20}^3$

It is given that,

  $1^3+2^3+3^3+\mathrm{...}+{20}^3$

Need to rewrite the series $1^3+2^3+3^3+\mathrm{...}+{20}^3$ using sigma notation,

Rewriting the given series by ${\left(n+1\right)}^3$ ,

Representation of the series by sigma notation by taking index $k=0$ to $k=20$ as

  $1^3+2^3+3^3+\mathrm{...}+{20}^3={\displaystyle \sum _{n=0}^{20}{\left(n+1\right)}^3}$

Therefore, Given series $1^3+2^3+3^3+\mathrm{...}+{20}^3$ using sigma notation is ${\displaystyle \sum _{n=0}^{20}{\left(n+1\right)}^3}$ .