小学六年级达标题

来源:百度知道 编辑:UC知道 时间:2024/06/30 20:09:48
问:3/4*5/6*7/8*……*19999/20000的乘积与0.01相比,那个大?
要有计算过程。

3/4*5/6*7/8*……*19999/20000的乘积与0.01相比,那个大?

分子中的3、5、7、9……9999分别与分母中的6、10、14、18、19998约分,
得到1/4*1/2*1/8*1/2*1/12*1/2*1/16……*19999/20000,
式中前四项的乘积为1/4*1/2*1/8*1/2=1/128,
且其后的数都是真分数,它们相乘一定小于1,
所以所有项的乘积一定小于1/128,
而0.01=1/100,1/128<1/100,
即1/384小于0.01.
因而
3/4*5/6*7/8*……*19999/20000的乘积小于0.01

0.01da

(3/4)*(4/5)*(5/6)*(19999/20000)
=(3*4*5*6.....19999)/(4*5*6*7*.....20000)
上下约去4*5*6*7....19999得:
3/20000=0.00015

因为0.01比0.00015大

所以与(3/4)*(4/5)*(5/6)*(19999/20000)相比,0.01大

当然是0.01!!!!!!!!!!!!!!!!!!!!!!!!!!
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0.01比分