Calculus Examples

$\sum_{k = 1}^{4} 2 k^{2} - 4$

Step 1

Expand the series for each value of $k$ .

$2 \cdot 1^{2} - 4 + 2 \cdot 2^{2} - 4 + 2 \cdot 3^{2} - 4 + 2 \cdot 4^{2} - 4$

Step 2

Simplify.

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Step 2.1

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

$2 \cdot 1 - 4 + 2 \cdot 2^{2} - 4 + 2 \cdot 3^{2} - 4 + 2 \cdot 4^{2} - 4$

Step 2.2

Multiply $2$ by $1$ .

$2 - 4 + 2 \cdot 2^{2} - 4 + 2 \cdot 3^{2} - 4 + 2 \cdot 4^{2} - 4$

Step 2.3

Subtract $4$ from $2$ .

$- 2 + 2 \cdot 2^{2} - 4 + 2 \cdot 3^{2} - 4 + 2 \cdot 4^{2} - 4$

Step 2.4

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

$- 2 + 2 \cdot 4 - 4 + 2 \cdot 3^{2} - 4 + 2 \cdot 4^{2} - 4$

Step 2.5

Multiply $2$ by $4$ .

$- 2 + 8 - 4 + 2 \cdot 3^{2} - 4 + 2 \cdot 4^{2} - 4$

Step 2.6

Subtract $4$ from $8$ .

$- 2 + 4 + 2 \cdot 3^{2} - 4 + 2 \cdot 4^{2} - 4$

Step 2.7

Add $- 2$ and $4$ .

$2 + 2 \cdot 3^{2} - 4 + 2 \cdot 4^{2} - 4$

Step 2.8

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

$2 + 2 \cdot 9 - 4 + 2 \cdot 4^{2} - 4$

Step 2.9

Multiply $2$ by $9$ .

$2 + 18 - 4 + 2 \cdot 4^{2} - 4$

Step 2.10

Subtract $4$ from $18$ .

$2 + 14 + 2 \cdot 4^{2} - 4$

Step 2.11

Add $2$ and $14$ .

$16 + 2 \cdot 4^{2} - 4$

Step 2.12

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

$16 + 2 \cdot 16 - 4$

Step 2.13

Multiply $2$ by $16$ .

$16 + 32 - 4$

Step 2.14

Subtract $4$ from $32$ .

$16 + 28$

Step 2.15

Add $16$ and $28$ .

$44$