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
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![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](/uploads/image/z/7206341-5-1.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D1%2F2%2Ca%28n%2B1%29%3Dan%5E2%2Ban%28n%E2%88%88N%2A%29%2C%E5%88%99m%3D1%2F%28a1%2B1%29%2B1%2F%28a2%2B1%29%2B...%2B1%2F%28a2013%2B1%29%E7%9A%84%E6%95%B4%E6%95%B0%E9%83%A8%E5%88%86%E6%98%AF%EF%BC%88%EF%BC%89A0+B1+C2+D3)
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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
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
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 >0
所以{an}是递增数列,
而a2=3/4 a3=21/16
当n>3时,an>a3=21/16
所以0
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