Calculus Examples

$\sum_{k = 0}^{3} k^{2} + 4$

Step 1

Expand the series for each value of $k$ .

$0^{2} + 4 + 1^{2} + 4 + 2^{2} + 4 + 3^{2} + 4$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Raise $0$ to the power of $2$ .

$0 + 4 + 1^{2} + 4 + 2^{2} + 4 + 3^{2} + 4$

Step 2.2

Add $0$ and $4$ .

$4 + 1^{2} + 4 + 2^{2} + 4 + 3^{2} + 4$

Step 2.3

Raise $1$ to the power of $2$ .

$4 + 1 + 4 + 2^{2} + 4 + 3^{2} + 4$

Step 2.4

Add $1$ and $4$ .

$4 + 5 + 2^{2} + 4 + 3^{2} + 4$

Step 2.5

Add $4$ and $5$ .

$9 + 2^{2} + 4 + 3^{2} + 4$

Step 2.6

Raise $2$ to the power of $2$ .

$9 + 4 + 4 + 3^{2} + 4$

Step 2.7

Add $4$ and $4$ .

$9 + 8 + 3^{2} + 4$

Step 2.8

Add $9$ and $8$ .

$17 + 3^{2} + 4$

Step 2.9

Raise $3$ to the power of $2$ .

$17 + 9 + 4$

Step 2.10

Add $9$ and $4$ .

$17 + 13$

Step 2.11

Add $17$ and $13$ .

$30$

$30$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$