Calculus Examples

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

Step 1

Expand the series for each value of $i$ .

$- 3 \cdot 2^{1 - 1} - 3 \cdot 2^{2 - 1} - 3 \cdot 2^{3 - 1} - 3 \cdot 2^{4 - 1}$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Subtract $1$ from $1$ .

$- 3 \cdot 2^{0} - 3 \cdot 2^{2 - 1} - 3 \cdot 2^{3 - 1} - 3 \cdot 2^{4 - 1}$

Step 2.2

Raise $2$ to the power of $0$ .

$- 3 \cdot 1 - 3 \cdot 2^{2 - 1} - 3 \cdot 2^{3 - 1} - 3 \cdot 2^{4 - 1}$

Step 2.3

Multiply $- 3$ by $1$ .

$- 3 - 3 \cdot 2^{2 - 1} - 3 \cdot 2^{3 - 1} - 3 \cdot 2^{4 - 1}$

Step 2.4

Subtract $1$ from $2$ .

$- 3 - 3 \cdot 2^{1} - 3 \cdot 2^{3 - 1} - 3 \cdot 2^{4 - 1}$

Step 2.5

Raise $2$ to the power of $1$ .

$- 3 - 3 \cdot 2 - 3 \cdot 2^{3 - 1} - 3 \cdot 2^{4 - 1}$

Step 2.6

Multiply $- 3$ by $2$ .

$- 3 - 6 - 3 \cdot 2^{3 - 1} - 3 \cdot 2^{4 - 1}$

Step 2.7

Subtract $6$ from $- 3$ .

$- 9 - 3 \cdot 2^{3 - 1} - 3 \cdot 2^{4 - 1}$

Step 2.8

Subtract $1$ from $3$ .

$- 9 - 3 \cdot 2^{2} - 3 \cdot 2^{4 - 1}$

Step 2.9

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

$- 9 - 3 \cdot 4 - 3 \cdot 2^{4 - 1}$

Step 2.10

Multiply $- 3$ by $4$ .

$- 9 - 12 - 3 \cdot 2^{4 - 1}$

Step 2.11

Subtract $12$ from $- 9$ .

$- 21 - 3 \cdot 2^{4 - 1}$

Step 2.12

Subtract $1$ from $4$ .

$- 21 - 3 \cdot 2^{3}$

Step 2.13

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

$- 21 - 3 \cdot 8$

Step 2.14

Multiply $- 3$ by $8$ .

$- 21 - 24$

Step 2.15

Subtract $24$ from $- 21$ .

$- 45$