Calculus Examples

$\sum_{n = 0}^{3} 5 m^{2} - 3 n$

Step 1

Expand the series for each value of $n$ .

$5 m^{2} - 3 \cdot 0 + 5 m^{2} - 3 \cdot 1 + 5 m^{2} - 3 \cdot 2 + 5 m^{2} - 3 \cdot 3$

Step 2

Substitute the values back and simplify $5 m^{2} - 3 \cdot 0 + 5 m^{2} - 3 \cdot 1 + 5 m^{2} - 3 \cdot 2 + 5 m^{2} - 3 \cdot 3$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $- 3$ by $0$ .

$5 m^{2} + 0 + 5 m^{2} - 3 \cdot 1 + 5 m^{2} - 3 \cdot 2 + 5 m^{2} - 3 \cdot 3$

Step 2.1.2

Multiply $- 3$ by $1$ .

$5 m^{2} + 0 + 5 m^{2} - 3 + 5 m^{2} - 3 \cdot 2 + 5 m^{2} - 3 \cdot 3$

Step 2.1.3

Multiply $- 3$ by $2$ .

$5 m^{2} + 0 + 5 m^{2} - 3 + 5 m^{2} - 6 + 5 m^{2} - 3 \cdot 3$

Step 2.1.4

Multiply $- 3$ by $3$ .

$5 m^{2} + 0 + 5 m^{2} - 3 + 5 m^{2} - 6 + 5 m^{2} - 9$

Step 2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1

Add $5 m^{2}$ and $0$ .

$5 m^{2} + 5 m^{2} - 3 + 5 m^{2} - 6 + 5 m^{2} - 9$

Step 2.2.2

Add $5 m^{2}$ and $5 m^{2}$ .

$10 m^{2} - 3 + 5 m^{2} - 6 + 5 m^{2} - 9$

Step 2.2.3

Add $10 m^{2}$ and $5 m^{2}$ .

$15 m^{2} - 3 - 6 + 5 m^{2} - 9$

Step 2.2.4

Add $15 m^{2}$ and $5 m^{2}$ .

$20 m^{2} - 3 - 6 - 9$

Step 2.2.5

Simplify by subtracting numbers.

Tap for more steps...

Step 2.2.5.1

Subtract $6$ from $- 3$ .

$20 m^{2} - 9 - 9$

Step 2.2.5.2

Subtract $9$ from $- 9$ .

$20 m^{2} - 18$