Calculus Examples

$\sum_{i = 1}^{16} 6 i$

Step 1

Factor $6$ out of the summation.

$6 \sum_{k = 1}^{16} i$

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.

$(6) (\frac{16 (16 + 1)}{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the expression.

Tap for more steps...

Step 4.1.1

Add $16$ and $1$ .

$6 \frac{16 \cdot 17}{2}$

Step 4.1.2

Multiply $16$ by $17$ .

$6 (\frac{272}{2})$

Step 4.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1

Factor $2$ out of $6$ .

$2 (3) \frac{272}{2}$

Step 4.2.2

Cancel the common factor.

$2 \cdot 3 \frac{272}{2}$

Step 4.2.3

Rewrite the expression.

$3 \cdot 272$

Step 4.3

Multiply $3$ by $272$ .

$816$