Calculus Examples

$\sum_{n = 0}^{3} 3^{2 - n}$

Step 1

Expand the series for each value of $n$ .

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

Step 2

Simplify.

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Step 2.1

Add $2$ and $0$ .

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

Step 2.2

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

$9 + 3^{2 - 1} + 3^{2 - 2} + 3^{2 - 3}$

Step 2.3

Subtract $1$ from $2$ .

$9 + 3^{1} + 3^{2 - 2} + 3^{2 - 3}$

Step 2.4

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

$9 + 3 + 3^{2 - 2} + 3^{2 - 3}$

Step 2.5

Add $9$ and $3$ .

$12 + 3^{2 - 2} + 3^{2 - 3}$

Step 2.6

Subtract $2$ from $2$ .

$12 + 3^{0} + 3^{2 - 3}$

Step 2.7

Raise $3$ to the power of $0$ .

$12 + 1 + 3^{2 - 3}$

Step 2.8

Add $12$ and $1$ .

$13 + 3^{2 - 3}$

Step 2.9

Subtract $3$ from $2$ .

$13 + 3^{- 1}$

Step 2.10

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

$13 + 0.\overline{3}$

Step 2.11

Add $13$ and $0.\overline{3}$ .

$13.\overline{3}$

$13.\overline{3}$

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