Calculus Examples

$10 + \sum_{x = 1}^{5} x^{3} - 1$

Step 1

Evaluate $\sum_{x = 1}^{5} x^{3} - 1$ .

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Step 1.1

The formula for the summation of a polynomial with degree $3$ is:

$\sum_{k = 1}^{n} k^{3} = \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 1.2

Substitute the values into the formula.

$\frac{5^{2} {(5 + 1)}^{2}}{4}$

Step 1.3

Simplify.

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Step 1.3.1

Simplify the numerator.

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Step 1.3.1.1

Add $5$ and $1$ .

$\frac{5^{2} \cdot 6^{2}}{4}$

Step 1.3.1.2

Raise $5$ to the power of $2$ .

$\frac{25 \cdot 6^{2}}{4}$

Step 1.3.1.3

Raise $6$ to the power of $2$ .

$\frac{25 \cdot 36}{4}$

Step 1.3.2

Simplify the expression.

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Step 1.3.2.1

Multiply $25$ by $36$ .

$\frac{900}{4}$

Step 1.3.2.2

Divide $900$ by $4$ .

$225$

Step 2

Add $10$ and $225$ .

$235$