Solve n*(n+1)(2n+1)/6

$$\frac { n \times ( n + 1 ) ( 2 n + 1 ) } { 6 }$$

Evaluate

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

Solution Steps

Use the distributive property to multiply n by n+1.

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

Apply the distributive property by multiplying each term of n^{2}+n by each term of 2n+1.

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

Combine n^{2} and 2n^{2} to get 3n^{2}.

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

Expand

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

Solution Steps

Use the distributive property to multiply n by n+1.

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

Apply the distributive property by multiplying each term of n^{2}+n by each term of 2n+1.

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

Combine n^{2} and 2n^{2} to get 3n^{2}.

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