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Popular >

expand (n(n+1)(2n+1))/3

Solution

expand

\frac{n ( n + 1 ) ( 2 n + 1 )}{3}

Solution

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

Solution steps

\frac{n ( n + 1 ) ( 2 n + 1 )}{3}

Expand

n (n + 1) (2 n + 1) : 2 n^{3} + 3 n^{2} + n

= \frac{2 n ^{3} + 3 n ^{2} + n}{3}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 n ^{3} + 3 n ^{2} + n}{3} = \frac{2 n ^{3}}{3} + \frac{3 n ^{2}}{3} + \frac{n}{3}

= \frac{2 n ^{3}}{3} + \frac{3 n ^{2}}{3} + \frac{n}{3}

Divide the numbers:

\frac{3}{3} = 1

= \frac{2 n ^{3}}{3} + n^{2} + \frac{n}{3}

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Frequently Asked Questions (FAQ)

What is expand (n(n+1)(2n+1))/3 ?
The solution to expand (n(n+1)(2n+1))/3 is (2n^3)/3+n^2+n/3