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

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

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

expand

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

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

Solution steps

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

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

sin (θ) - cos (θ) (sin (θ) + cos (θ))

(ln ∣ tan (x) + sec (x) ∣ - sin (x)) (sin (x))

(1 + \frac{1}{1 + t ^{2}}) (1 + t^{2})^{2}

\frac{ln ( \frac{( 1 + x + h )}{1 + x} )}{h}

\frac{1459}{( 1 + x ) ^{10}}

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