Calculus Examples

$\frac{lim_{x \to 8} 8}{n^{3}} \cdot (\frac{n (n + 1) (2 n + 1)}{6})$

Step 1

Evaluate the limit of $8$ which is constant as $x$ approaches $8$ .

$\frac{8}{n^{3}} \cdot \frac{n (n + 1) (2 n + 1)}{6}$

Step 2

Simplify the answer.

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Step 2.1

Combine.

$\frac{8 (n (n + 1) (2 n + 1))}{n^{3} \cdot 6}$

Step 2.2

Cancel the common factor of $8$ and $6$ .

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Step 2.2.1

Factor $2$ out of $8 (n (n + 1) (2 n + 1))$ .

$\frac{2 (4 (n (n + 1) (2 n + 1)))}{n^{3} \cdot 6}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $n^{3} \cdot 6$ .

$\frac{2 (4 (n (n + 1) (2 n + 1)))}{2 (n^{3} \cdot 3)}$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 (4 (n (n + 1) (2 n + 1)))}{2 (n^{3} \cdot 3)}$

Step 2.2.2.3

Rewrite the expression.

$\frac{4 (n (n + 1) (2 n + 1))}{n^{3} \cdot 3}$

Step 2.3

Move $3$ to the left of $n^{3}$ .

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