Calculus Examples

$\sum_{i = 1}^{4} 2 + 3^{i - 1}$

Step 1

Expand the series for each value of $i$ .

$2 + 3^{1 - 1} + 2 + 3^{2 - 1} + 2 + 3^{3 - 1} + 2 + 3^{4 - 1}$

Step 2

Simplify.

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Step 2.1

Subtract $1$ from $1$ .

$2 + 3^{0} + 2 + 3^{2 - 1} + 2 + 3^{3 - 1} + 2 + 3^{4 - 1}$

Step 2.2

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

$2 + 1 + 2 + 3^{2 - 1} + 2 + 3^{3 - 1} + 2 + 3^{4 - 1}$

Step 2.3

Add $2$ and $1$ .

$3 + 2 + 3^{2 - 1} + 2 + 3^{3 - 1} + 2 + 3^{4 - 1}$

Step 2.4

Subtract $1$ from $2$ .

$3 + 2 + 3^{1} + 2 + 3^{3 - 1} + 2 + 3^{4 - 1}$

Step 2.5

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

$3 + 2 + 3 + 2 + 3^{3 - 1} + 2 + 3^{4 - 1}$

Step 2.6

Add $2$ and $3$ .

$3 + 5 + 2 + 3^{3 - 1} + 2 + 3^{4 - 1}$

Step 2.7

Add $3$ and $5$ .

$8 + 2 + 3^{3 - 1} + 2 + 3^{4 - 1}$

Step 2.8

Subtract $1$ from $3$ .

$8 + 2 + 3^{2} + 2 + 3^{4 - 1}$

Step 2.9

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

$8 + 2 + 9 + 2 + 3^{4 - 1}$

Step 2.10

Add $2$ and $9$ .

$8 + 11 + 2 + 3^{4 - 1}$

Step 2.11

Add $8$ and $11$ .

$19 + 2 + 3^{4 - 1}$

Step 2.12

Subtract $1$ from $4$ .

$19 + 2 + 3^{3}$

Step 2.13

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

$19 + 2 + 27$

Step 2.14

Add $2$ and $27$ .

$19 + 29$

Step 2.15

Add $19$ and $29$ .

$48$