Calculus Examples

$\sum_{i = 1}^{100} 3 i$

Step 1

Factor $3$ out of the summation.

$3 \sum_{k = 1}^{100} i$

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.

$(3) (\frac{100 (100 + 1)}{2})$

Step 4

Simplify.

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Step 4.1

Add $100$ and $1$ .

$3 \frac{100 \cdot 101}{2}$

Step 4.2

Multiply $100$ by $101$ .

$3 (\frac{10100}{2})$

Step 4.3

Divide $10100$ by $2$ .

$3 \cdot 5050$

Step 4.4

Multiply $3$ by $5050$ .

$15150$