Calculus Examples

$\sum_{k = 1}^{n} \frac{k^{2}}{5}$

Step 1

The formula for the summation of a polynomial with degree $2$ is:

$\sum_{k = 1}^{n} k^{2} = \frac{n (n + 1) (2 n + 1)}{6}$

Step 2

Substitute the values into the formula and make sure to multiply by the front term.

$(\frac{1}{5}) (\frac{n (n + 1) (2 n + 1)}{6})$

Step 3

Multiply $(\frac{1}{5}) (\frac{n (n + 1) (2 n + 1)}{6})$ .

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Step 3.1

Multiply $\frac{1}{5}$ by $\frac{n (n + 1) (2 n + 1)}{6}$ .

$\frac{n (n + 1) (2 n + 1)}{5 \cdot 6}$

Step 3.2

Multiply $5$ by $6$ .

$\frac{n (n + 1) (2 n + 1)}{30}$