Calculus Examples

$\sum_{x = 4}^{12} \frac{1}{4} \cdot 3^{k - 1}$

Step 1

Simplify the summation.

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Step 1.1

Combine $\frac{1}{4}$ and $3^{k - 1}$ .

$\frac{3^{k - 1}}{4}$

Step 1.2

Rewrite the summation.

$\sum_{x = 4}^{12} \frac{3^{k - 1}}{4}$

Step 2

Expand the series for each value of $x$ .

$\frac{3^{k - 1}}{4} + \frac{3^{k - 1}}{4} + \frac{3^{k - 1}}{4} + \dots + \frac{3^{k - 1}}{4}$

Step 3

Simplify the expanded form.

$\frac{3^{1 + k}}{4}$