Calculus Examples

$\sum_{n = 1}^{4} 4 n - 3$

Step 1

Expand the series for each value of $n$ .

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

Step 2

Simplify.

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Step 2.1

Multiply $4$ by $1$ .

$4 - 3 + 4 \cdot 2 - 3 + 4 \cdot 3 - 3 + 4 \cdot 4 - 3$

Step 2.2

Subtract $3$ from $4$ .

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

Step 2.3

Multiply $4$ by $2$ .

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

Step 2.4

Subtract $3$ from $8$ .

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

Step 2.5

Add $1$ and $5$ .

$6 + 4 \cdot 3 - 3 + 4 \cdot 4 - 3$

Step 2.6

Multiply $4$ by $3$ .

$6 + 12 - 3 + 4 \cdot 4 - 3$

Step 2.7

Subtract $3$ from $12$ .

$6 + 9 + 4 \cdot 4 - 3$

Step 2.8

Add $6$ and $9$ .

$15 + 4 \cdot 4 - 3$

Step 2.9

Multiply $4$ by $4$ .

$15 + 16 - 3$

Step 2.10

Subtract $3$ from $16$ .

$15 + 13$

Step 2.11

Add $15$ and $13$ .

$28$