Q. 19 - Calculus

Question

Fill in the blanks to complete each sum formula:

$\sum _{k=1}^n{k}^3=\underline{ }$

Step-by-Step Solution

Answer

 The complete sum formula is $\sum _{k=1}^n{k}^3=\underline{\frac{n^2{(n+1)}^2}{4}}·$

Step 1. Given information.

Given incomplete sum formula is following.

$\sum _{k=1}^n{k}^3=\underline{ }$

Step 2. Explanation.

If n is a positive integer, then by the induction method sigma notation for $k^3$ will be following.

$\sum _{k=1}^n{k}^3=\frac{n^2{(n+1)}^2}{4}$