Solve 1/n^3[(n+1)(2n+1)/6]

$$\frac { 1 } { n ^ { 3 } } [ \frac { ( n + 1 ) ( 2 n + 1 ) } { 6 } ]$$

Evaluate

$$\frac{\left(n+1\right)\left(2n+1\right)}{6n^{3}}$$

Short Solution Steps

Use the distributive property to multiply n+1 by 2n+1 and combine like terms.

$$\frac{1}{n^{3}}\times \frac{2n^{2}+3n+1}{6}$$

Multiply \frac{1}{n^{3}} times \frac{2n^{2}+3n+1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2n^{2}+3n+1}{n^{3}\times 6}$$

Expand

$$\frac{2n^{2}+3n+1}{6n^{3}}$$

Short Solution Steps

Use the distributive property to multiply n+1 by 2n+1 and combine like terms.

$$\frac{1}{n^{3}}\times \frac{2n^{2}+3n+1}{6}$$

Multiply \frac{1}{n^{3}} times \frac{2n^{2}+3n+1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2n^{2}+3n+1}{n^{3}\times 6}$$