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Popular >

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

Solution

expand

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

Solution

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

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Frequently Asked Questions (FAQ)

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