Precalculus Examples

$\sum_{k = 4}^{7} \sqrt{2 k - 1}$

Step 1

Expand the series for each value of $k$ .

$\sqrt{2 \cdot 4 - 1} + \sqrt{2 \cdot 5 - 1} + \sqrt{2 \cdot 6 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2

Simplify.

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Step 2.1

Multiply $2$ by $4$ .

$\sqrt{8 - 1} + \sqrt{2 \cdot 5 - 1} + \sqrt{2 \cdot 6 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2.2

Subtract $1$ from $8$ .

$\sqrt{7} + \sqrt{2 \cdot 5 - 1} + \sqrt{2 \cdot 6 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2.3

Evaluate the root.

$2.64575131 + \sqrt{2 \cdot 5 - 1} + \sqrt{2 \cdot 6 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2.4

Multiply $2$ by $5$ .

$2.64575131 + \sqrt{10 - 1} + \sqrt{2 \cdot 6 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2.5

Subtract $1$ from $10$ .

$2.64575131 + \sqrt{9} + \sqrt{2 \cdot 6 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2.6

Evaluate the root.

$2.64575131 + 3 + \sqrt{2 \cdot 6 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2.7

Add $2.64575131$ and $3$ .

$5.64575131 + \sqrt{2 \cdot 6 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2.8

Multiply $2$ by $6$ .

$5.64575131 + \sqrt{12 - 1} + \sqrt{2 \cdot 7 - 1}$

Step 2.9

Subtract $1$ from $12$ .

$5.64575131 + \sqrt{11} + \sqrt{2 \cdot 7 - 1}$

Step 2.10

Evaluate the root.

$5.64575131 + 3.31662479 + \sqrt{2 \cdot 7 - 1}$

Step 2.11

Add $5.64575131$ and $3.31662479$ .

$8.9623761 + \sqrt{2 \cdot 7 - 1}$

Step 2.12

Multiply $2$ by $7$ .

$8.9623761 + \sqrt{14 - 1}$

Step 2.13

Subtract $1$ from $14$ .

$8.9623761 + \sqrt{13}$

Step 2.14

Evaluate the root.

$8.9623761 + 3.60555127$

Step 2.15

Add $8.9623761$ and $3.60555127$ .

$12.56792737$