展开 (4n(-1)^n+2n(-1)^{n-1}-(-1)^{n-1}-1)/4

解答

展开

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

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

求解步骤

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

使用分式法则:

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

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

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

数字相除:

\frac{4}{4} = 1

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

消掉

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

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

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