展开-((-1)^n-1)/(pi^2n^2)

解答

展开

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

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

求解步骤

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

使用分式法则:

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

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

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

去除括号:

(a) = a, - (- a) = a

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

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