1/1*3+1/3*5+1/5*7+.+1/2013*2015

Question

1/1*3+1/3*5+1/5*7+.+1/2013*2015

Answer 1

通项公式是:
1/(2n-1)(2n+1)=[1/(2n-1)-1/(2n+1)]/2
所以,所求可以化为:
[1-1/3+1/3-1/5+...+1/2013-1/2015]/2
=(1-1/2015)/2
=1007/2015