Calculus Examples

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

Expand the series for each value of $n$ .

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

Simplify.

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Multiply $3$ by $1$ .

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

Subtract $1$ from $3$ .

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

Multiply $3$ by $2$ .

$2 + 6 - 1 + 3 \cdot 3 - 1 + 3 \cdot 4 - 1$

Subtract $1$ from $6$ .

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

Add $2$ and $5$ .

$7 + 3 \cdot 3 - 1 + 3 \cdot 4 - 1$

Multiply $3$ by $3$ .

$7 + 9 - 1 + 3 \cdot 4 - 1$

Subtract $1$ from $9$ .

$7 + 8 + 3 \cdot 4 - 1$

Add $7$ and $8$ .

$15 + 3 \cdot 4 - 1$

Multiply $3$ by $4$ .

$15 + 12 - 1$

Subtract $1$ from $12$ .

$15 + 11$

Add $15$ and $11$ .

$26$