Calculus Examples

$4 \sum_{i = 0}^{3} 1 + 2 i^{2}$

Step 1

Expand the series for each value of $i$ .

$4 (1 + 2 \cdot 0^{2} + 1 + 2 \cdot 1^{2} + 1 + 2 \cdot 2^{2} + 1 + 2 \cdot 3^{2})$

Step 2

Simplify.

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Step 2.1

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

$4 (1 + 2 \cdot 0 + 1 + 2 \cdot 1^{2} + 1 + 2 \cdot 2^{2} + 1 + 2 \cdot 3^{2})$

Step 2.2

Multiply $2$ by $0$ .

$4 (1 + 0 + 1 + 2 \cdot 1^{2} + 1 + 2 \cdot 2^{2} + 1 + 2 \cdot 3^{2})$

Step 2.3

Add $1$ and $0$ .

$4 (1 + 1 + 2 \cdot 1^{2} + 1 + 2 \cdot 2^{2} + 1 + 2 \cdot 3^{2})$

Step 2.4

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

$4 (1 + 1 + 2 \cdot 1 + 1 + 2 \cdot 2^{2} + 1 + 2 \cdot 3^{2})$

Step 2.5

Multiply $2$ by $1$ .

$4 (1 + 1 + 2 + 1 + 2 \cdot 2^{2} + 1 + 2 \cdot 3^{2})$

Step 2.6

Add $1$ and $2$ .

$4 (1 + 3 + 1 + 2 \cdot 2^{2} + 1 + 2 \cdot 3^{2})$

Step 2.7

Add $1$ and $3$ .

$4 (4 + 1 + 2 \cdot 2^{2} + 1 + 2 \cdot 3^{2})$

Step 2.8

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

$4 (4 + 1 + 2 \cdot 4 + 1 + 2 \cdot 3^{2})$

Step 2.9

Multiply $2$ by $4$ .

$4 (4 + 1 + 8 + 1 + 2 \cdot 3^{2})$

Step 2.10

Add $1$ and $8$ .

$4 (4 + 9 + 1 + 2 \cdot 3^{2})$

Step 2.11

Add $4$ and $9$ .

$4 (13 + 1 + 2 \cdot 3^{2})$

Step 2.12

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

$4 (13 + 1 + 2 \cdot 9)$

Step 2.13

Multiply $2$ by $9$ .

$4 (13 + 1 + 18)$

Step 2.14

Add $1$ and $18$ .

$4 (13 + 19)$

Step 2.15

Add $13$ and $19$ .

$4 \cdot 32$

Step 2.16

Multiply $4$ by $32$ .

$128$