Precalculus Examples

$\sum_{k = 3}^{6} 2^{k}$

Step 1

Expand the series for each value of $k$ .

$2^{3} + 2^{4} + 2^{5} + 2^{6}$

Step 2

Simplify.

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Step 2.1

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

$8 + 2^{4} + 2^{5} + 2^{6}$

Step 2.2

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

$8 + 16 + 2^{5} + 2^{6}$

Step 2.3

Add $8$ and $16$ .

$24 + 2^{5} + 2^{6}$

Step 2.4

Raise $2$ to the power of $5$ .

$24 + 32 + 2^{6}$

Step 2.5

Add $24$ and $32$ .

$56 + 2^{6}$

Step 2.6

Raise $2$ to the power of $6$ .

$56 + 64$

Step 2.7

Add $56$ and $64$ .

$120$

$120$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$