What is expand ((-1)^{n+1}(n-1)(n+2))/n ?

The solution to expand ((-1)^{n+1}(n-1)(n+2))/n is (-1)^{n+1}n+(-1)^{n+1}-(2(-1)^{n+1})/n

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expand ((-1)^{n+1}(n-1)(n+2))/n

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

5 (\cdot + 2 - 8 + \cdot = - 16)

\frac{( 3 x + 12 y ) ( 3 x + 28 y )}{16}

e^{y} (- e^{- y} y - e^{- y})

\frac{i wl}{R ( 1 - w ^{2} l c ) + i wl}

f^{(4)} 6 (6 ln (5 x) + 11)

What is expand ((-1)^{n+1}(n-1)(n+2))/n ?
The solution to expand ((-1)^{n+1}(n-1)(n+2))/n is (-1)^{n+1}n+(-1)^{n+1}-(2(-1)^{n+1})/n