Question

急！一个数学问题！！！只有15分钟！

1|1*3+1|3*5+1|5*7+1|7*9……+1|2001*2003 把步骤也写出来、
一乘三分之一加三乘五分之一、依次往下、谢谢了、跪求、马上

Answer 1

1/1*3 = (1/2)*(1-1/3)

1/3*5 = (1/2)*(1/3-1/5)

1/5*7 = (1/2)*(1/5-1/7)

……

1/1*3 +1/3*5 +……+1/2001*2003

=1/2(1-1/3+1/3-1/5+……+ 1/2001- 1/2003)

=1/2(1-1/2003)

=1001/2003

Answer 2

因为 1/[n(n+2)] = (1/2)*[1/n - 1/(n+2)]

所以
1/(1*3) + 1/(3*5) + 1/(5*7) + ... + 1/(2001*2003)

= (1/2)*[(1/1 - 1/3) + (1/3 - 1/5)+ (1/5 - 1/7)
+ + ... + (1/2001 - 1/2003)]

= (1/2)*[1/1 - 1/2003)

=(1/2)*(2002/2003)

= 1001/2003

Answer 3

1/1*3+1/3*5+1/5*7……1/2001*2003
=(1/2)*2(1/1*3+1/3*5+1/5*7……1/2001*2003)
= (1/2)*(2/1*3+2/3*5+2/5*7……2/2001*2003)
=(1/2)*(1/1-1/3+1/3-1/5+1/5-1/7……1/2001-1/2003)
=(1/2)*(2002/2003)
=1001/2003

Answer 4

告诉你一个算式：a*b/1=a/1*b/1-(a-b/1) (ab不相邻，且a小于b)

Answer 5

=1/[2（1/1-1/3）]+.......+1/[2(1/2001-1/2003)]

=(1/2)*(1/1-1/3 + 1/3-1/5 +......... + 1/2001 -1/2003 )

=(1/2)*(1-1/2003)

=(2003-1)/(2003*2)

=1001/2003