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

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

expand

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

\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}

\frac{e ^{- s}}{s ( s + 1 ) ^{3}}

(x + 1) \cdot ln^{2} (x + 1)

K (1 + \frac{1}{I s} + d s)

e^{3 t} h (t - 1)

\frac{x ^{2} + 4}{x ^{2} ( x - 4 )}

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