Chapter 8, Problem 13CR

To determine

To find: the sigma notation of the series and sum of the series.

Answer to Problem 13CR

Sigma notation of the series $3{\left(1\right)}^2+3{\left(2\right)}^2+3{\left(3\right)}^2\mathrm{..........}+3{\left(9\right)}^2$ is $\underset{\_}{3{\displaystyle \sum _{k=1}^9{k}^2}}$ and sum of the series is $\underset{\_}{855}$ .

Explanation of Solution

Given information:

The series which needs to be represent as sigma notation is as follows

  $3{\left(1\right)}^2+3{\left(2\right)}^2+3{\left(3\right)}^2\mathrm{..........}+3{\left(9\right)}^2$

Calculation:

The series which needs to be represent as sigma notation is as follows

  $3{\left(1\right)}^2+3{\left(2\right)}^2+3{\left(3\right)}^2\mathrm{..........}+3{\left(9\right)}^2$

  $=3\left({\left(1\right)}^2+{\left(2\right)}^2+{\left(3\right)}^2\mathrm{..........}+{\left(9\right)}^2\right)$

  $=3{\displaystyle \sum _{k=1}^9{k}^2}$

Calculating sum using utility

  

Hence sigma notation of the series $3{\left(1\right)}^2+3{\left(2\right)}^2+3{\left(3\right)}^2\mathrm{..........}+3{\left(9\right)}^2$ is $\underset{\_}{3{\displaystyle \sum _{k=1}^9{k}^2}}$ and sum of the series is $\underset{\_}{855}$ .