Calculus Examples

$\sum_{i = 1}^{24} 4 i$

Step 1

Factor $4$ out of the summation.

$4 \sum_{k = 1}^{24} i$

Step 2

The formula for the summation of a polynomial with degree $1$ is:

$\sum_{k = 1}^{n} i = \frac{n (n + 1)}{2}$

Step 3

Substitute the values into the formula and make sure to multiply by the front term.

$(4) (\frac{24 (24 + 1)}{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the expression.

Tap for more steps...

Step 4.1.1

Add $24$ and $1$ .

$4 \frac{24 \cdot 25}{2}$

Step 4.1.2

Multiply $24$ by $25$ .

$4 (\frac{600}{2})$

Step 4.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1

Factor $2$ out of $4$ .

$2 (2) \frac{600}{2}$

Step 4.2.2

Cancel the common factor.

$2 \cdot 2 \frac{600}{2}$

Step 4.2.3

Rewrite the expression.

$2 \cdot 600$

Step 4.3

Multiply $2$ by $600$ .

$1200$