Calculus Examples

$\sum_{i = 1}^{8} 4 {(\frac{1}{2})}^{n}$

Step 1

Simplify the summation.

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Step 1.1

Apply the product rule to $\frac{1}{2}$ .

$4 \frac{1^{n}}{2^{n}}$

Step 1.2

One to any power is one.

$4 \frac{1}{2^{n}}$

Step 1.3

Combine $4$ and $\frac{1}{2^{n}}$ .

$\frac{4}{2^{n}}$

Step 1.4

Rewrite the summation.

$\sum_{i = 1}^{8} \frac{4}{2^{n}}$

$\sum_{i = 1}^{8} \frac{4}{2^{n}}$

Step 2

The formula for the summation of a constant is:

$\sum_{k = 1}^{n} c = c n$

Step 3

Substitute the values into the formula.

$(\frac{4}{2^{n}}) (8)$

Step 4

Multiply $(\frac{4}{2^{n}}) (8)$ .

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Step 4.1

Combine $\frac{4}{2^{n}}$ and $8$ .

$\frac{4 \cdot 8}{2^{n}}$

Step 4.2

Multiply $4$ by $8$ .

$\frac{32}{2^{n}}$

$\frac{32}{2^{n}}$

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