Calculus Examples

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

Step 1

Expand the series for each value of $m$ .

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

Step 2

Simplify.

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Step 2.1

Multiply $2$ by $1$ .

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

Step 2.2

Add $2$ and $1$ .

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

Step 2.3

Subtract $1$ from $1$ .

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

Step 2.4

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

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

Step 2.5

Multiply $2$ by $2$ .

$1 + {(4 + 1)}^{2 - 1} + {(2 \cdot 3 + 1)}^{3 - 1}$

Step 2.6

Add $4$ and $1$ .

$1 + 5^{2 - 1} + {(2 \cdot 3 + 1)}^{3 - 1}$

Step 2.7

Subtract $1$ from $2$ .

$1 + 5^{1} + {(2 \cdot 3 + 1)}^{3 - 1}$

Step 2.8

Raise $5$ to the power of $1$ .

$1 + 5 + {(2 \cdot 3 + 1)}^{3 - 1}$

Step 2.9

Add $1$ and $5$ .

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

Step 2.10

Multiply $2$ by $3$ .

$6 + {(6 + 1)}^{3 - 1}$

Step 2.11

Add $6$ and $1$ .

$6 + 7^{3 - 1}$

Step 2.12

Subtract $1$ from $3$ .

$6 + 7^{2}$

Step 2.13

Raise $7$ to the power of $2$ .

$6 + 49$

Step 2.14

Add $6$ and $49$ .

$55$