Precalculus Examples

$\sum_{i = 0}^{3} 2^{i} i$

Step 1

Expand the series for each value of $i$ .

$2^{0} \cdot 0 + 2^{1} \cdot 1 + 2^{2} \cdot 2 + 2^{3} \cdot 3$

Step 2

Simplify.

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Step 2.1

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

$1 \cdot 0 + 2^{1} \cdot 1 + 2^{2} \cdot 2 + 2^{3} \cdot 3$

Step 2.2

Multiply $1$ by $0$ .

$0 + 2^{1} \cdot 1 + 2^{2} \cdot 2 + 2^{3} \cdot 3$

Step 2.3

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

$0 + 2 \cdot 1 + 2^{2} \cdot 2 + 2^{3} \cdot 3$

Step 2.4

Multiply $2$ by $1$ .

$0 + 2 + 2^{2} \cdot 2 + 2^{3} \cdot 3$

Step 2.5

Add $0$ and $2$ .

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

Step 2.6

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

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

Step 2.7

Multiply $4$ by $2$ .

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

Step 2.8

Add $2$ and $8$ .

$10 + 2^{3} \cdot 3$

Step 2.9

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

$10 + 8 \cdot 3$

Step 2.10

Multiply $8$ by $3$ .

$10 + 24$

Step 2.11

Add $10$ and $24$ .

$34$