Question

1/1*3+1/3*5+1/5*7+1/7*9+.+1/2009*2011 要求最好写清计算过程,和思路,

Answer 1

1/[n*(n+2)]=[1/n-1/(n+2)]/2,

所以原式=(1-1/3+1/3-1/5+1/5-1/7+……+1/2009-1/2011)/2=(1-1/2011)/2=1005/2011