Calculus Examples

$\sum_{n = 3}^{5} n^{2} - 2^{n}$

Step 1

Expand the series for each value of $n$ .

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

Step 2

Simplify.

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Step 2.1

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

$9 - 2^{3} + 4^{2} - 2^{4} + 5^{2} - 2^{5}$

Step 2.2

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

$9 - 1 \cdot 8 + 4^{2} - 2^{4} + 5^{2} - 2^{5}$

Step 2.3

Multiply $- 1$ by $8$ .

$9 - 8 + 4^{2} - 2^{4} + 5^{2} - 2^{5}$

Step 2.4

Subtract $8$ from $9$ .

$1 + 4^{2} - 2^{4} + 5^{2} - 2^{5}$

Step 2.5

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

$1 + 16 - 2^{4} + 5^{2} - 2^{5}$

Step 2.6

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

$1 + 16 - 1 \cdot 16 + 5^{2} - 2^{5}$

Step 2.7

Multiply $- 1$ by $16$ .

$1 + 16 - 16 + 5^{2} - 2^{5}$

Step 2.8

Subtract $16$ from $16$ .

$1 + 0 + 5^{2} - 2^{5}$

Step 2.9

Add $1$ and $0$ .

$1 + 5^{2} - 2^{5}$

Step 2.10

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

$1 + 25 - 2^{5}$

Step 2.11

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

$1 + 25 - 1 \cdot 32$

Step 2.12

Multiply $- 1$ by $32$ .

$1 + 25 - 32$

Step 2.13

Subtract $32$ from $25$ .

$1 - 7$

Step 2.14

Subtract $7$ from $1$ .

$- 6$

$- 6$

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