Question

Fill in the blanks to complete each sum formula:

$\sum _{k=1}^n{k}^2=\underline{}$

Short answer

The complete sum formula is$\sum _{k=1}^n{k}^2=\underline{\frac{n(n+1)(2n+1)}{6}}.$

Step-by-step solution

Step 1. Given information.

Given incomplete sum formula is following.

$\sum _{k=1}^n{k}^2=\underline{}$

Step 2. Explanation.

If n is a positive integer, then by the induction method sigma notation for $k^2$will be following.

role="math" localid="1648775750262" $\sum _{k=1}^n{k}^2=\frac{n(n+1)(2n+1)}{6}$