What is expand ((-1)^n(-pi^2n^2+6))/(n^3) ?

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

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expand ((-1)^n(-pi^2n^2+6))/(n^3)

expand

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

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

Solution steps

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

Expand

(- 1)^{n} (- π^{2} n^{2} + 6) : - π^{2} (- 1)^{n} n^{2} + 6 (- 1)^{n}

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

Apply the fraction rule:

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

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

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

Cancel

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

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

\frac{x}{( x y + 1 ) ( x ^{2} + 1 )}

(\frac{4}{( 3 - 5 ) ^{2}})^{2}

l im x \Rightarrow 5 (3 x^{2} + x - 2)

\frac{( 2 s + 2 + s e ^{- s - 1} )}{s ( s + 1 ) ^{2}}

\frac{- 2 x - 9}{( x - 2 ) ( x - 4 ) ( x + 3 )}

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