(1+1/2+1/3+...+1/1994)(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)(1/2+1/3+...+1/1994)怎样算?

来源：学生作业帮助网编辑：六六作业网时间：2024/12/25 01:59:28

(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)怎样算?(1+1/2+1/3

(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)怎样算?
(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)怎样算?

(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)怎样算?
令 1/2+1/3+...+1/1994 = a
则
(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)
= (1+a)*(a+1/1995) - (1+a+1/1995)*a
= (a + a² + 1/1995 + a/1995) - (a + a² + a/1995)
= 1/1995

答：
设a=1/2+1/3+...+1/1994，b=1/2+1/3+...+1/1995，则：b-a=1/1995
(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)
=(1+a)*b-(1+b)*a
=b+ab-a-ab
=b-a

全部展开

答：
设a=1/2+1/3+...+1/1994，b=1/2+1/3+...+1/1995，则：b-a=1/1995
(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)
=(1+a)*b-(1+b)*a
=b+ab-a-ab
=b-a
=1/1995
所以：
(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)=1/1995

收起

199*(1-1/2)*(1-1/3)*(1-1/4)*.*(1-1/199) 要过程 199×(1-2/1)×(1-3/1)×(1-4/1)×．．．÷（1-199/1）=? 1+2+3+.+199+200=（ 2,-1,3,-1,4,-1,第199个数是 2,--1,3,-1,4,-1---第199个数是多少 1/1*2+1/2*3+1/3*4+1/4*5+.+1/199*200wu 1/1*2+1/2*3+1/3*4+1/4*5+...+1/199*200 1/1*2+1/2*3+1/3*4+1/4*5+^+1/199*200=? 简算.1/1X2+1/2X3+1/3X4+1/4X5+.+1/199X200, (200+199+198+…+3+2+1)-(199+197+195+…+5+3+1)= 1/1乘2+1/2乘3+1/3乘4.+1/199乘200 简便计算:1/1×2+1/2×3+1/3×4+...+1/199×200 1/1*2+1/2*3+1/3*4+.+1/199*200 1/1*2+1/2*3+1/3*4+...+1/199*200 计算1/2+1/2+3+1/2+3+4+.1/2+3+4+.+199+200 怎样计算3/1*2+3/2*3+.+3/198*199+3/199*200 2×3/1+3×4/1+4×5/1+5×6/1+.199×200/1=? 1-1/2+1/3-1/4+1/5+1/6+1/7-----------+1/199-1/200jijiji