Precalculus Examples

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

Step 1

Expand the series for each value of $i$ .

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

Step 2

Simplify.

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Step 2.1

Raise $1$ to the power of $3$ .

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

Step 2.2

Multiply $3$ by $1$ .

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

Step 2.3

Multiply $2$ by $1$ .

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

Step 2.4

Add $3$ and $2$ .

$5 - 4 + 3 \cdot 2^{3} + 2 \cdot 2 - 4 + 3 \cdot 3^{3} + 2 \cdot 3 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.5

Subtract $4$ from $5$ .

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

Step 2.6

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

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

Step 2.7

Multiply $3$ by $8$ .

$1 + 24 + 2 \cdot 2 - 4 + 3 \cdot 3^{3} + 2 \cdot 3 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.8

Multiply $2$ by $2$ .

$1 + 24 + 4 - 4 + 3 \cdot 3^{3} + 2 \cdot 3 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.9

Add $24$ and $4$ .

$1 + 28 - 4 + 3 \cdot 3^{3} + 2 \cdot 3 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.10

Subtract $4$ from $28$ .

$1 + 24 + 3 \cdot 3^{3} + 2 \cdot 3 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.11

Add $1$ and $24$ .

$25 + 3 \cdot 3^{3} + 2 \cdot 3 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.12

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

$25 + 3 \cdot 27 + 2 \cdot 3 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.13

Multiply $3$ by $27$ .

$25 + 81 + 2 \cdot 3 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.14

Multiply $2$ by $3$ .

$25 + 81 + 6 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.15

Add $81$ and $6$ .

$25 + 87 - 4 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.16

Subtract $4$ from $87$ .

$25 + 83 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.17

Add $25$ and $83$ .

$108 + 3 \cdot 4^{3} + 2 \cdot 4 - 4$

Step 2.18

Raise $4$ to the power of $3$ .

$108 + 3 \cdot 64 + 2 \cdot 4 - 4$

Step 2.19

Multiply $3$ by $64$ .

$108 + 192 + 2 \cdot 4 - 4$

Step 2.20

Multiply $2$ by $4$ .

$108 + 192 + 8 - 4$

Step 2.21

Add $192$ and $8$ .

$108 + 200 - 4$

Step 2.22

Subtract $4$ from $200$ .

$108 + 196$

Step 2.23

Add $108$ and $196$ .

$304$