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

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

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simplify (n(n+1)(2n+1))/6-(n(n+1))/2

simplify

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

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

Solution steps

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

Least Common Multiplier of

6, 2 : 6

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

n (n + 1) (2 n + 1) - n (n + 1) \cdot 3 : 2 n^{3} - 2 n

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

Cancel

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

= \frac{n ( n + 1 ) ( n - 1 )}{3}

- \frac{1}{5} \cdot 10

- 8 (n + 4) = - 32 - 8 n

2 b^{2} - b - 7 = 14

2 + 3 t = 1 + t^{2}

\frac{e ^{\frac{c}{m} t}}{e ^{\frac{c}{m} t}}

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