数列{an}满足a1=1/2,a(n+1)=an^2+an(n∈N*),则m=1/(a1+1)+1/(a2+1)+...+1/(a2013+1)的整数部分是()A0 B1 C2 D3

问题描述:

数列{an}满足a1=1/2,a(n+1)=an^2+an(n∈N*),则m=1/(a1+1)+1/(a2+1)+...+1/(a2013+1)的整数部分是()
A0 B1 C2 D3

1/a(n+1)=1/(an^2+an)=1/an-1/(an+1)1/(an+1)= 1/an-1/a(n+1)1/(a1+1)+1/(a2+1)+...+1/(a2013+1)=(1/a1-1/a2)+(1/a2-1/a3)+...+(1/a2013-1/a2014)=1/a1 - 1/a2014=2-1/a2014因为a(n+1)=an^2 +an所以a(n+1) -an=an^2 ...