展开 (2(-1)^n-2)/(pi^3n^3)-((-1)^n)/(pin)

解答

展开

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

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

求解步骤

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

使用分式法则:

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

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

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

e x p an d (\frac{π}{2} - x) tan (x)

e x p an d \frac{3 ( - s ^{2} + 3 ) - 2 s}{6 ( s ^{3} + 2 s ^{2} - 6 )}

e x p an d \frac{4 s ^{2} + 5 s + 6}{s ( s ^{3} + 7 s ^{2} + 13 s + 2 )}

e x p an d y (y = 4 x - x^{2})

e x p an d (0, - 2) y (- 3, 4)