Calculus Examples

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

Step 1

Expand the series for each value of $k$ .

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

Step 2

Simplify.

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Step 2.1

Raise $0$ to the power of $4$ .

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

Step 2.2

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

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

Step 2.3

Add $0$ and $0$ .

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

Step 2.4

Raise $1$ to the power of $4$ .

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

Step 2.5

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

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

Step 2.6

Add $1$ and $1$ .

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

Step 2.7

Add $0$ and $2$ .

$2 + 2^{4} + 2^{2}$

Step 2.8

Raise $2$ to the power of $4$ .

$2 + 16 + 2^{2}$

Step 2.9

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

$2 + 16 + 4$

Step 2.10

Add $16$ and $4$ .

$2 + 20$

Step 2.11

Add $2$ and $20$ .

$22$

$22$

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