Precalculus Examples

$\sum_{x = 1}^{5} {(\frac{1}{3})}^{k}$

Step 1

Simplify the summation.

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Step 1.1

Apply the product rule to $\frac{1}{3}$ .

$\frac{1^{k}}{3^{k}}$

Step 1.2

One to any power is one.

$\frac{1}{3^{k}}$

Step 1.3

Rewrite the summation.

$\sum_{x = 1}^{5} \frac{1}{3^{k}}$

Step 2

Expand the series for each value of $x$ .

$\frac{1}{3^{k}} + \frac{1}{3^{k}} + \frac{1}{3^{k}} + \dots + \frac{1}{3^{k}}$

Step 3

Simplify the expanded form.

$\frac{5}{3^{k}}$