Calculus Examples

$\sum_{n = 2}^{4} 3 n^{2} - 5 n + 7$

Step 1

Expand the series for each value of $n$ .

$3 \cdot 2^{2} - 5 \cdot 2 + 7 + 3 \cdot 3^{2} - 5 \cdot 3 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2

Simplify.

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Step 2.1

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

$3 \cdot 4 - 5 \cdot 2 + 7 + 3 \cdot 3^{2} - 5 \cdot 3 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.2

Multiply $3$ by $4$ .

$12 - 5 \cdot 2 + 7 + 3 \cdot 3^{2} - 5 \cdot 3 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.3

Multiply $- 5$ by $2$ .

$12 - 10 + 7 + 3 \cdot 3^{2} - 5 \cdot 3 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.4

Subtract $10$ from $12$ .

$2 + 7 + 3 \cdot 3^{2} - 5 \cdot 3 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.5

Add $2$ and $7$ .

$9 + 3 \cdot 3^{2} - 5 \cdot 3 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.6

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

$9 + 3 \cdot 9 - 5 \cdot 3 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.7

Multiply $3$ by $9$ .

$9 + 27 - 5 \cdot 3 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.8

Multiply $- 5$ by $3$ .

$9 + 27 - 15 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.9

Subtract $15$ from $27$ .

$9 + 12 + 7 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.10

Add $12$ and $7$ .

$9 + 19 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.11

Add $9$ and $19$ .

$28 + 3 \cdot 4^{2} - 5 \cdot 4 + 7$

Step 2.12

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

$28 + 3 \cdot 16 - 5 \cdot 4 + 7$

Step 2.13

Multiply $3$ by $16$ .

$28 + 48 - 5 \cdot 4 + 7$

Step 2.14

Multiply $- 5$ by $4$ .

$28 + 48 - 20 + 7$

Step 2.15

Subtract $20$ from $48$ .

$28 + 28 + 7$

Step 2.16

Add $28$ and $7$ .

$28 + 35$

Step 2.17

Add $28$ and $35$ .

$63$