Chapter 11.4, Problem 3OE

To determine

To explain:

Limits of summation for ${\displaystyle \sum _{m=2}^5\left(4m^2-3\right)}$

Answer to Problem 3OE

Upper limit is $5$ and lower limit is $2$ for ${\displaystyle \sum _{m=2}^5\left(4m^2-3\right)}$ .

Explanation of Solution

Give information:

Expression:

  ${\displaystyle \sum _{m=2}^5\left(4m^2-3\right)}$

The formula for finding series is,

  ${\displaystyle \sum _{i=1}^{n}C}$

Where,

  $i=$ index of summation.

  $C=$ Summand of the given expression.

  $n=$ upper limit of summation.

  $1=$ lower limit of summation.

After comparing to the summation formula,

In given expression ${\displaystyle \sum _{m=2}^5\left(4m^2-3\right)}$ ,

Limits for ${\displaystyle \sum _{m=2}^5\left(4m^2-3\right)}$ is $5$ and $m=2$ .

Therefore, Limits for ${\displaystyle \sum _{m=2}^5\left(4m^2-3\right)}$ is $2$ to $5$ .