(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2000)(1/2000-1)
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(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2000)(1/2000-1)
![(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2000)(1/2000-1)](/uploads/image/z/20045042-26-2.jpg?t=%281-1%2F2%29%281%2F3-1%29%281-1%2F4%29%281%2F5-1%29.%281-1%2F2000%29%281%2F2000-1%29)
(1-1/2)(1/3-1)(1-1/4)(1/5-1)……(1-1/2000)
=(1-1/2)(-1)(1-1/3)(1-1/4)(-1)(1-1/5)……(-1)(1-1/1999)(1-1/2000)
=(1-1/2)(1-1/3)(1-1/4)(1-1/5)……(1-1/49)(1-1/2000) 因为24个(-1)相乘为1
=(1/2)*(2/3)*(3/4)……*(1998/1999)*(1999/2000)
=1/2000
所以(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2000)(1/2000-1)
=(1/2000)*(1/2000-1)
=(1-1/2)(-1)(1-1/3)(1-1/4)(-1)(1-1/5)……(-1)(1-1/1999)(1-1/2000)
=(1-1/2)(1-1/3)(1-1/4)(1-1/5)……(1-1/49)(1-1/2000) 因为24个(-1)相乘为1
=(1/2)*(2/3)*(3/4)……*(1998/1999)*(1999/2000)
=1/2000
所以(1-1/2)(1/3-1)(1-1/4)(1/5-1).(1-1/2000)(1/2000-1)
=(1/2000)*(1/2000-1)
(1/2+1/3+...+1/2000)*(1+1/2+...+1/1999)-(1+1/2+...+1/2000)*(
(1-1/2)+(1/2-1/3)+(1/3-1/4).+(1/1999-1/2000)
1/2+1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7+.1/1999*1/2000得多
如何计算:(1-1/2*2)(1-1/3*3)(1-1/4*4)(1-1/5*5)、、、(1-1/2000*2000)拜
1/2+1/3+1/4+1/5+1/6+1/7+……+1/2000+1/2001
1/2+1/3+1/4+1/5+\\\\\\\\\+1/2000=?
1/1*2+1/2*3+1/3*4+...+1/2000*1/2001=
1/1*2+1/2*3+1/3*4+.+1/1998*1999+1/1999*2000
1/1×2+1/2×3+1/3×4+...+1/1998×1999+1/1999×2000
(1-1/2)X(1-1/3)X(1-1/4)X.X(1-1/1999)X(1/2000)
1/2*1/3+1/3*1/4+.+1/1999*1/2000
求证1/1方+1/2方+1/3方+1/4方+1/5方+...+1/2000方