用简便方法计算 (1/2²-1)(1/3²-1)(1/4²-1)...(1/10²-)……(1/10²-1)
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用简便方法计算 (1/2²-1)(1/3²-1)(1/4²-1)...(1/10²-)……(1/10²-1)
用简便方法计算 (1/2²-1)(1/3²-1)(1/4²-1)...(1/10²-
)
……(1/10²-1)
用简便方法计算 (1/2²-1)(1/3²-1)(1/4²-1)...(1/10²-)……(1/10²-1)
1/2²-1 = (1/2 +1)(1/2 - 1) = 3/2 * -1/2
1/3²-1 = 4/3 * -2/3
1/4²-1 = 5/4 * -3/4
.
1/10²-1 = 11/10 * -9/10
由于是相乘,3/2 跟 -2/3抵消成 -1,每两项剩下一个 -1,共10个全部抵消
最后剩下 1/2 * 11/10 = 11/20