( 1+17/1)*(1+17/2)*(1+17/3)*.*(1+17/19)/(1+19/1)*(1+19/2)*(1+19/30*.*(1+19/17)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 05:03:38
( 1+17/1)*(1+17/2)*(1+17/3)*.*(1+17/19)/(1+19/1)*(1+19/2)*(1+19/30*.*(1+19/17)=?

( 1+17/1)*(1+17/2)*(1+17/3)*.*(1+17/19)/(1+19/1)*(1+19/2)*(1+19/30*.*(1+19/17)=?
( 1+17/1)*(1+17/2)*(1+17/3)*.*(1+17/19)/(1+19/1)*(1+19/2)*(1+19/30*.*(1+19/17)=?

( 1+17/1)*(1+17/2)*(1+17/3)*.*(1+17/19)/(1+19/1)*(1+19/2)*(1+19/30*.*(1+19/17)=?
原式 = [18/1 * 19/2 * 20/3 .* 36/19] / [20/1 * 21/2 * 22/3 ...* 36/17] =
[18/1 * 19/2 * 20/3 .* 36/19] * [1/20 * 2/21 * 3/22 *...* 17/36] =
36!/ 36!=
1