What is expand (n(n+1)(2n+1))/2 ?

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

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\frac{1}{s ( s ^{2} + 9 )}

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\frac{2 x ^{3} - 6 x ^{2}}{( x - 2 ) ^{2}}

(- e^{- t} sin (t) + e^{- t} cos (t))^{2}

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