Chapter 12.1, Problem 63E

To determine

Find the sum by using sigma notation.

Answer to Problem 63E

The sum by the sigma notation is ${\displaystyle \sum _{k=1}^{10}{k}^2}$ .

Explanation of Solution

Given:

It is given in the question that the sum of the few terms are $1^2+2^2+3^2+\mathrm{............}+{10}^2$ .

Concept Used:

In this, use the concept of understand the pattern of the term and write by using sigma notation.

Calculation:

Here, the term is $1^2+2^2+3^2+\mathrm{............}+{10}^2$ .

It is seen in the term that k varies from $1to10$ for the expression $k^2$ .

So, there are many possible answers. A natural way to write is ${\displaystyle \sum _{k=1}^{10}{k}^2}$ .

Conclusion:

The sum by the sigma notation is ${\displaystyle \sum _{k=1}^{10}{k}^2}$ .