Calculus Examples

$\sum_{n = 1}^{4} 2 n + 1$

Step 1

Expand the series for each value of $n$ .

$2 \cdot 1 + 1 + 2 \cdot 2 + 1 + 2 \cdot 3 + 1 + 2 \cdot 4 + 1$

Step 2

Simplify.

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Step 2.1

Multiply $2$ by $1$ .

$2 + 1 + 2 \cdot 2 + 1 + 2 \cdot 3 + 1 + 2 \cdot 4 + 1$

Step 2.2

Add $2$ and $1$ .

$3 + 2 \cdot 2 + 1 + 2 \cdot 3 + 1 + 2 \cdot 4 + 1$

Step 2.3

Multiply $2$ by $2$ .

$3 + 4 + 1 + 2 \cdot 3 + 1 + 2 \cdot 4 + 1$

Step 2.4

Add $4$ and $1$ .

$3 + 5 + 2 \cdot 3 + 1 + 2 \cdot 4 + 1$

Step 2.5

Add $3$ and $5$ .

$8 + 2 \cdot 3 + 1 + 2 \cdot 4 + 1$

Step 2.6

Multiply $2$ by $3$ .

$8 + 6 + 1 + 2 \cdot 4 + 1$

Step 2.7

Add $6$ and $1$ .

$8 + 7 + 2 \cdot 4 + 1$

Step 2.8

Add $8$ and $7$ .

$15 + 2 \cdot 4 + 1$

Step 2.9

Multiply $2$ by $4$ .

$15 + 8 + 1$

Step 2.10

Add $8$ and $1$ .

$15 + 9$

Step 2.11

Add $15$ and $9$ .

$24$