Precalculus Examples

$\sum_{i = 1}^{300} 2 i$

Step 1

Factor $2$ out of the summation.

$2 \sum_{k = 1}^{300} i$

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.

$(2) (\frac{300 (300 + 1)}{2})$

Step 4

Simplify.

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Step 4.1

Simplify the expression.

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Step 4.1.1

Add $300$ and $1$ .

$2 \frac{300 \cdot 301}{2}$

Step 4.1.2

Multiply $300$ by $301$ .

$2 (\frac{90300}{2})$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Cancel the common factor.

$2 (\frac{90300}{2})$

Step 4.2.2

Rewrite the expression.

$90300$