Precalculus Examples

$\sum_{i = 1}^{4} 2 i + 6 i^{2}$

Step 1

Expand the series for each value of $i$ .

$2 \cdot 1 + 6 \cdot 1^{2} + 2 \cdot 2 + 6 \cdot 2^{2} + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2

Simplify.

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Step 2.1

Multiply $2$ by $1$ .

$2 + 6 \cdot 1^{2} + 2 \cdot 2 + 6 \cdot 2^{2} + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.2

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

$2 + 6 \cdot 1 + 2 \cdot 2 + 6 \cdot 2^{2} + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.3

Multiply $6$ by $1$ .

$2 + 6 + 2 \cdot 2 + 6 \cdot 2^{2} + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.4

Add $2$ and $6$ .

$8 + 2 \cdot 2 + 6 \cdot 2^{2} + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.5

Multiply $2$ by $2$ .

$8 + 4 + 6 \cdot 2^{2} + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.6

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

$8 + 4 + 6 \cdot 4 + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.7

Multiply $6$ by $4$ .

$8 + 4 + 24 + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.8

Add $4$ and $24$ .

$8 + 28 + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.9

Add $8$ and $28$ .

$36 + 2 \cdot 3 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.10

Multiply $2$ by $3$ .

$36 + 6 + 6 \cdot 3^{2} + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.11

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

$36 + 6 + 6 \cdot 9 + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.12

Multiply $6$ by $9$ .

$36 + 6 + 54 + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.13

Add $6$ and $54$ .

$36 + 60 + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.14

Add $36$ and $60$ .

$96 + 2 \cdot 4 + 6 \cdot 4^{2}$

Step 2.15

Multiply $2$ by $4$ .

$96 + 8 + 6 \cdot 4^{2}$

Step 2.16

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

$96 + 8 + 6 \cdot 16$

Step 2.17

Multiply $6$ by $16$ .

$96 + 8 + 96$

Step 2.18

Add $8$ and $96$ .

$96 + 104$

Step 2.19

Add $96$ and $104$ .

$200$