Question

1/1*2+2/1*2*3+3/1*2*3*4+4/1*2*3*4*5+----+9/1*2*3*5*6*7*8*9*10

请告诉计算过程。

Answer 1

=1/2+2/6+3/24+4/120+5/720+...+9/362880
=(2*3*4*5*6*7*8*9+3*4*5*6*7*8*9+.........+9)/1*2*3*4*5*6*7*8*9
=(2+1)(3+1)(4+1)(5+1)(6+1)(7+1)(8+1)(9+1)/1*2*3*4*5*6*7*8*9
=(3*4*5*6*7*8*9*10)/1*2*3*4*5*6*7*8*9
=10/2
=5

Answer 2

因为(n-1)/n!=n/n!-1/n!=1/(n-1)!-1/n!,(n>=2)
1/2+2/1*2*3+3/1*2*3*4+...+9/1*2*3*4*5*6*7*8*9*10=1-1/2+1/2!-1/3!+……+1/9!-1/10!
=1-1/10!

Answer 3

9/1*2*3*4*5*6*7*8*9*10=9/10!=(10-1)/10!=1/9!-1/10!
每一个都可以这样化的,!是阶乘
答案:1-1/10!

Answer 4

(n-1)/n!=1/(n-1)!-1/n!
1/2+2/1*2*3+3/1*2*3*4+...+9/1*2*3*4*5*6*7*8*9*10=1/1!-1/2!+1/2!-1/3!+...1/9!-1/10!=1-1/10!

Answer 5

1/2=(2-1)/2
1/2+2/1*2*3=(2*3-1)/1*2*3=5/6
1/2+1/3+1/8+.....+9/1*2*3*4*5*6*7*8*9*10....
=(1*1*2*3*4....n-1)/1*2*3*4....n
=(2*3*4....n-1)/2*3*4....n
也可=1-1/2*3*4....n