用简便方法计算 (1/2²-1)(1/3²-1)(1/4²-1)...(1/10²-

问题描述:

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