Precalculus Examples

$\sum_{k = 3}^{5} k^{2} + 2 k + 2$

Step 1

Expand the series for each value of $k$ .

$3^{2} + 2 \cdot 3 + 2 + 4^{2} + 2 \cdot 4 + 2 + 5^{2} + 2 \cdot 5 + 2$

Step 2

Simplify.

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Step 2.1

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

$9 + 2 \cdot 3 + 2 + 4^{2} + 2 \cdot 4 + 2 + 5^{2} + 2 \cdot 5 + 2$

Step 2.2

Multiply $2$ by $3$ .

$9 + 6 + 2 + 4^{2} + 2 \cdot 4 + 2 + 5^{2} + 2 \cdot 5 + 2$

Step 2.3

Add $9$ and $6$ .

$15 + 2 + 4^{2} + 2 \cdot 4 + 2 + 5^{2} + 2 \cdot 5 + 2$

Step 2.4

Add $15$ and $2$ .

$17 + 4^{2} + 2 \cdot 4 + 2 + 5^{2} + 2 \cdot 5 + 2$

Step 2.5

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

$17 + 16 + 2 \cdot 4 + 2 + 5^{2} + 2 \cdot 5 + 2$

Step 2.6

Multiply $2$ by $4$ .

$17 + 16 + 8 + 2 + 5^{2} + 2 \cdot 5 + 2$

Step 2.7

Add $16$ and $8$ .

$17 + 24 + 2 + 5^{2} + 2 \cdot 5 + 2$

Step 2.8

Add $24$ and $2$ .

$17 + 26 + 5^{2} + 2 \cdot 5 + 2$

Step 2.9

Add $17$ and $26$ .

$43 + 5^{2} + 2 \cdot 5 + 2$

Step 2.10

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

$43 + 25 + 2 \cdot 5 + 2$

Step 2.11

Multiply $2$ by $5$ .

$43 + 25 + 10 + 2$

Step 2.12

Add $25$ and $10$ .

$43 + 35 + 2$

Step 2.13

Add $35$ and $2$ .

$43 + 37$

Step 2.14

Add $43$ and $37$ .

$80$