expandir (8(2(-1)^n-pi^2(-1)^nn^2-2))/(pin^3)

Solução

expandir

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

\frac{16 ( - 1 ) ^{n}}{π n ^{3}} - \frac{8 π ( - 1 ) ^{n}}{n} - \frac{16}{π n ^{3}}

Passos da solução

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

Expandir

8 (2 (- 1)^{n} - π^{2} (- 1)^{n} n^{2} - 2) : 16 (- 1)^{n} - 8 π^{2} (- 1)^{n} n^{2} - 16

= \frac{16 ( - 1 ) ^{n} - 8 π ^{2} ( - 1 ) ^{n} n ^{2} - 16}{π n ^{3}}

Aplicar as propriedades das frações:

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

\frac{16 ( - 1 ) ^{n} - 8 π ^{2} ( - 1 ) ^{n} n ^{2} - 16}{π n ^{3}} = \frac{16 ( - 1 ) ^{n}}{π n ^{3}} - \frac{8 π ^{2} ( - 1 ) ^{n} n ^{2}}{π n ^{3}} - \frac{16}{π n ^{3}}

= \frac{16 ( - 1 ) ^{n}}{π n ^{3}} - \frac{8 π ^{2} ( - 1 ) ^{n} n ^{2}}{π n ^{3}} - \frac{16}{π n ^{3}}

Cancelar

\frac{8 π ^{2} ( - 1 ) ^{n} n ^{2}}{π n ^{3}} : \frac{8 π ( - 1 ) ^{n}}{n}

= \frac{16 ( - 1 ) ^{n}}{π n ^{3}} - \frac{8 π ( - 1 ) ^{n}}{n} - \frac{16}{π n ^{3}}

e x p an d \frac{1}{\frac{16 x ^{2}}{n ^{2}} - \frac{8 x}{n} + 1}

e x p an d \frac{37.68}{3}

e x p an d \frac{20 ( 110 - 12010 )}{3}

e x p an d 2 x - 4 cos (x^{2} + 3 x) (2 x + 3)

e x p an d (- 0.5) (9 - x) (\frac{2}{3} x - 4)