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

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

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

expand

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

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

Solution steps

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

Expand

\frac{1}{6} n (n + 1) (2 n + 1) : \frac{1}{6} n (2 n^{2} + 3 n + 1)

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

Apply the distributive law:

m (a + b + c) = ma + mb + m c

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

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

Simplify

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

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

- \frac{1}{( x + 4 ) ^{2}}

(x + x) \cdot (x)

\frac{- x + 2 + ( x + 1 ) x - 2}{x + 1}

\frac{2 e ^{- 2 s} - 7 s ^{3} + 2 s ^{2} - 2 s}{s ( - s ^{3} + s ^{2} + 2 )}

\frac{1}{x ( x + a )}

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