Calculus Examples

$\sum_{m = 1}^{4} 5 m^{2} + 4$

Step 1

Expand the series for each value of $m$ .

$5 \cdot 1^{2} + 4 + 5 \cdot 2^{2} + 4 + 5 \cdot 3^{2} + 4 + 5 \cdot 4^{2} + 4$

Step 2

Simplify.

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Step 2.1

Raise $1$ to the power of $2$ .

$5 \cdot 1 + 4 + 5 \cdot 2^{2} + 4 + 5 \cdot 3^{2} + 4 + 5 \cdot 4^{2} + 4$

Step 2.2

Multiply $5$ by $1$ .

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

Step 2.3

Add $5$ and $4$ .

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

Step 2.4

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

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

Step 2.5

Multiply $5$ by $4$ .

$9 + 20 + 4 + 5 \cdot 3^{2} + 4 + 5 \cdot 4^{2} + 4$

Step 2.6

Add $20$ and $4$ .

$9 + 24 + 5 \cdot 3^{2} + 4 + 5 \cdot 4^{2} + 4$

Step 2.7

Add $9$ and $24$ .

$33 + 5 \cdot 3^{2} + 4 + 5 \cdot 4^{2} + 4$

Step 2.8

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

$33 + 5 \cdot 9 + 4 + 5 \cdot 4^{2} + 4$

Step 2.9

Multiply $5$ by $9$ .

$33 + 45 + 4 + 5 \cdot 4^{2} + 4$

Step 2.10

Add $45$ and $4$ .

$33 + 49 + 5 \cdot 4^{2} + 4$

Step 2.11

Add $33$ and $49$ .

$82 + 5 \cdot 4^{2} + 4$

Step 2.12

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

$82 + 5 \cdot 16 + 4$

Step 2.13

Multiply $5$ by $16$ .

$82 + 80 + 4$

Step 2.14

Add $80$ and $4$ .

$82 + 84$

Step 2.15

Add $82$ and $84$ .

$166$