Precalculus Examples

$\sum_{m = 1}^{7} m^{2}$

Step 1

The formula for the summation of a polynomial with degree $2$ is:

$\sum_{k = 1}^{n} k^{2} = \frac{n (n + 1) (2 n + 1)}{6}$

Step 2

Substitute the values into the formula.

$\frac{7 (7 + 1) (2 \cdot 7 + 1)}{6}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Add $7$ and $1$ .

$\frac{7 \cdot 8 (2 \cdot 7 + 1)}{6}$

Step 3.1.2

Combine exponents.

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Step 3.1.2.1

Multiply $7$ by $8$ .

$\frac{56 (2 \cdot 7 + 1)}{6}$

Step 3.1.2.2

Multiply $2$ by $7$ .

$\frac{56 (14 + 1)}{6}$

Step 3.1.3

Add $14$ and $1$ .

$\frac{56 \cdot 15}{6}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Multiply $56$ by $15$ .

$\frac{840}{6}$

Step 3.2.2

Divide $840$ by $6$ .

$140$