What is expand (n(n+1)(2n+1))/6+(n+1) ?

The solution to expand (n(n+1)(2n+1))/6+(n+1) is (n^3)/3+(n^2)/2+n/6+n+1

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expand (n(n+1)(2n+1))/6+(n+1)

expand

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

\frac{n ^{3}}{3} + \frac{n ^{2}}{2} + \frac{n}{6} + n + 1

Solution steps

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

Remove parentheses:

(a) = a

= \frac{n ( n + 1 ) ( 2 n + 1 )}{6} + n + 1

Expand

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

= \frac{2 n ^{3} + 3 n ^{2} + n}{6} + n + 1

Apply the fraction rule:

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

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

= \frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6} + n + 1

Cancel

\frac{2 n ^{3}}{6} : \frac{n ^{3}}{3}

= \frac{n ^{3}}{3} + \frac{3 n ^{2}}{6} + \frac{n}{6} + n + 1

Cancel

\frac{3 n ^{2}}{6} : \frac{n ^{2}}{2}

= \frac{n ^{3}}{3} + \frac{n ^{2}}{2} + \frac{n}{6} + n + 1

- 5 x > 15

\frac{X}{3} + 1 < 4

- \frac{8}{9} + 9

12 x^{2} + 31 x + 20

11 x^{2} + 2 x - 9 = 0

What is expand (n(n+1)(2n+1))/6+(n+1) ?
The solution to expand (n(n+1)(2n+1))/6+(n+1) is (n^3)/3+(n^2)/2+n/6+n+1