数列{an}中,an=1/n(n+1),{an}的前n项和为2009/2010,则项数n为

题目

数列{an}中,an=1/n(n+1),{an}的前n项和为2009/2010,则项数n为
A2008 B2009 C2010 C2011

答案

an=[(n+1)-n]/n(n+1)
=(n+1)/n(n+1)-1/n(n+1)
=1/n-1/(n+1)
所以Sn=1-1/2+1/2-1/3+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
=2009/2010
所以n=2009