Calculus Examples

$\sum_{i = 1}^{4} 6^{i - 1}$

Step 1

Expand the series for each value of $i$ .

$6^{1 - 1} + 6^{2 - 1} + 6^{3 - 1} + 6^{4 - 1}$

Step 2

Simplify.

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Step 2.1

Subtract $1$ from $1$ .

$6^{0} + 6^{2 - 1} + 6^{3 - 1} + 6^{4 - 1}$

Step 2.2

Raise $6$ to the power of $0$ .

$1 + 6^{2 - 1} + 6^{3 - 1} + 6^{4 - 1}$

Step 2.3

Subtract $1$ from $2$ .

$1 + 6^{1} + 6^{3 - 1} + 6^{4 - 1}$

Step 2.4

Raise $6$ to the power of $1$ .

$1 + 6 + 6^{3 - 1} + 6^{4 - 1}$

Step 2.5

Add $1$ and $6$ .

$7 + 6^{3 - 1} + 6^{4 - 1}$

Step 2.6

Subtract $1$ from $3$ .

$7 + 6^{2} + 6^{4 - 1}$

Step 2.7

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

$7 + 36 + 6^{4 - 1}$

Step 2.8

Add $7$ and $36$ .

$43 + 6^{4 - 1}$

Step 2.9

Subtract $1$ from $4$ .

$43 + 6^{3}$

Step 2.10

Raise $6$ to the power of $3$ .

$43 + 216$

Step 2.11

Add $43$ and $216$ .

$259$

$259$

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