erweitern (4(-pi^2(-1)^nn^2+2(-1)^n-2))/(pin^3)

Lösung

erweitern

\frac{4 ( - π ^{2} ( - 1 ) ^{n} n ^{2} + 2 ( - 1 ) ^{n} - 2 )}{π n ^{3}}

- \frac{4 π ( - 1 ) ^{n}}{n} + \frac{8 ( - 1 ) ^{n}}{π n ^{3}} - \frac{8}{π n ^{3}}

Schritte zur Lösung

\frac{4 ( - π ^{2} ( - 1 ) ^{n} n ^{2} + 2 ( - 1 ) ^{n} - 2 )}{π n ^{3}}

Multipliziere aus

4 (- π^{2} (- 1)^{n} n^{2} + 2 (- 1)^{n} - 2) : - 4 π^{2} (- 1)^{n} n^{2} + 8 (- 1)^{n} - 8

= \frac{- 4 π ^{2} ( - 1 ) ^{n} n ^{2} + 8 ( - 1 ) ^{n} - 8}{π n ^{3}}

Wende Bruchregel an:

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

\frac{- 4 π ^{2} ( - 1 ) ^{n} n ^{2} + 8 ( - 1 ) ^{n} - 8}{π n ^{3}} = - \frac{4 π ^{2} ( - 1 ) ^{n} n ^{2}}{π n ^{3}} + \frac{8 ( - 1 ) ^{n}}{π n ^{3}} - \frac{8}{π n ^{3}}

= - \frac{4 π ^{2} ( - 1 ) ^{n} n ^{2}}{π n ^{3}} + \frac{8 ( - 1 ) ^{n}}{π n ^{3}} - \frac{8}{π n ^{3}}

Streiche

\frac{4 π ^{2} ( - 1 ) ^{n} n ^{2}}{π n ^{3}} : \frac{4 π ( - 1 ) ^{n}}{n}

= - \frac{4 π ( - 1 ) ^{n}}{n} + \frac{8 ( - 1 ) ^{n}}{π n ^{3}} - \frac{8}{π n ^{3}}

e x p an d (t^{2} - 1) d t

e x p an d (2, - 1) P (- 3, 7)

e x p an d (x^{- 2} y = \frac{3 x ^{2}}{2} + c) \frac{1}{x ^{- 2}}

e x p an d 8 (e^{- 0.4 x} - e^{- 0.6 x})

e x p an d (\frac{x + 2}{x})^{4}