Calculus Examples

$\sum_{m = 1}^{3} 2 {(3)}^{m - 1}$

Step 1

Expand the series for each value of $m$ .

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

Step 2

Simplify.

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Step 2.1

Subtract $1$ from $1$ .

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

Step 2.2

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

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

Step 2.3

Multiply $2$ by $1$ .

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

Step 2.4

Subtract $1$ from $2$ .

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

Step 2.5

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

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

Step 2.6

Multiply $2$ by $3$ .

$2 + 6 + 2 \cdot 3^{3 - 1}$

Step 2.7

Add $2$ and $6$ .

$8 + 2 \cdot 3^{3 - 1}$

Step 2.8

Subtract $1$ from $3$ .

$8 + 2 \cdot 3^{2}$

Step 2.9

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

$8 + 2 \cdot 9$

Step 2.10

Multiply $2$ by $9$ .

$8 + 18$

Step 2.11

Add $8$ and $18$ .

$26$