展开 (4(n+1)(2n+1))/(n^2)

解答

展开

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

8 + \frac{12}{n} + \frac{4}{n ^{2}}

求解步骤

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

乘开

4 (n + 1) (2 n + 1) : 8 n^{2} + 12 n + 4

= \frac{8 n ^{2} + 12 n + 4}{n ^{2}}

使用分式法则:

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

\frac{8 n ^{2} + 12 n + 4}{n ^{2}} = \frac{8 n ^{2}}{n ^{2}} + \frac{12 n}{n ^{2}} + \frac{4}{n ^{2}}

= \frac{8 n ^{2}}{n ^{2}} + \frac{12 n}{n ^{2}} + \frac{4}{n ^{2}}

消掉

\frac{8 n ^{2}}{n ^{2}} : 8

= 8 + \frac{12 n}{n ^{2}} + \frac{4}{n ^{2}}

消掉

\frac{12 n}{n ^{2}} : \frac{12}{n}

= 8 + \frac{12}{n} + \frac{4}{n ^{2}}

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s im pl i f y 6 (1 - x - \frac{1 - x ^{2}}{2})

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