Calculus Examples

$\sum_{i = 4}^{7} 2^{i - 7}$

Step 1

Expand the series for each value of $i$ .

$2^{4 - 7} + 2^{5 - 7} + 2^{6 - 7} + 2^{7 - 7}$

Step 2

Simplify.

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Step 2.1

Subtract $7$ from $4$ .

$2^{- 3} + 2^{5 - 7} + 2^{6 - 7} + 2^{7 - 7}$

Step 2.2

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

$0.125 + 2^{5 - 7} + 2^{6 - 7} + 2^{7 - 7}$

Step 2.3

Subtract $7$ from $5$ .

$0.125 + 2^{- 2} + 2^{6 - 7} + 2^{7 - 7}$

Step 2.4

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

$0.125 + 0.25 + 2^{6 - 7} + 2^{7 - 7}$

Step 2.5

Add $0.125$ and $0.25$ .

$0.375 + 2^{6 - 7} + 2^{7 - 7}$

Step 2.6

Subtract $7$ from $6$ .

$0.375 + 2^{- 1} + 2^{7 - 7}$

Step 2.7

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

$0.375 + 0.5 + 2^{7 - 7}$

Step 2.8

Add $0.375$ and $0.5$ .

$0.875 + 2^{7 - 7}$

Step 2.9

Subtract $7$ from $7$ .

$0.875 + 2^{0}$

Step 2.10

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

$0.875 + 1$

Step 2.11

Add $0.875$ and $1$ .

$1.875$

$1.875$

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