Calculus Examples

$\sum_{k = 2}^{5} k^{2} + k - 2$

Step 1

Expand the series for each value of $k$ .

$2^{2} + 2 - 2 + 3^{2} + 3 - 2 + 4^{2} + 4 - 2 + 5^{2} + 5 - 2$

Step 2

Simplify.

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Step 2.1

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

$4 + 2 - 2 + 3^{2} + 3 - 2 + 4^{2} + 4 - 2 + 5^{2} + 5 - 2$

Step 2.2

Add $4$ and $2$ .

$6 - 2 + 3^{2} + 3 - 2 + 4^{2} + 4 - 2 + 5^{2} + 5 - 2$

Step 2.3

Subtract $2$ from $6$ .

$4 + 3^{2} + 3 - 2 + 4^{2} + 4 - 2 + 5^{2} + 5 - 2$

Step 2.4

Raise $3$ to the power of $2$ .

$4 + 9 + 3 - 2 + 4^{2} + 4 - 2 + 5^{2} + 5 - 2$

Step 2.5

Add $9$ and $3$ .

$4 + 12 - 2 + 4^{2} + 4 - 2 + 5^{2} + 5 - 2$

Step 2.6

Subtract $2$ from $12$ .

$4 + 10 + 4^{2} + 4 - 2 + 5^{2} + 5 - 2$

Step 2.7

Add $4$ and $10$ .

$14 + 4^{2} + 4 - 2 + 5^{2} + 5 - 2$

Step 2.8

Raise $4$ to the power of $2$ .

$14 + 16 + 4 - 2 + 5^{2} + 5 - 2$

Step 2.9

Add $16$ and $4$ .

$14 + 20 - 2 + 5^{2} + 5 - 2$

Step 2.10

Subtract $2$ from $20$ .

$14 + 18 + 5^{2} + 5 - 2$

Step 2.11

Add $14$ and $18$ .

$32 + 5^{2} + 5 - 2$

Step 2.12

Raise $5$ to the power of $2$ .

$32 + 25 + 5 - 2$

Step 2.13

Add $25$ and $5$ .

$32 + 30 - 2$

Step 2.14

Subtract $2$ from $30$ .

$32 + 28$

Step 2.15

Add $32$ and $28$ .

$60$