已知数列求{an}
已知数列求{an}满足:an+1=(an-1)/(an+1),且a3=-1005/1004,求a2008...
已知数列求{an}满足:an+1=(an-1)/(an+1),且a3=-1005/1004,求a2008
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a(n+1)=(an-1)/(an+1),
a3=(a2-1)/(a2+1)=-1005/1004,得a2=-1/2009
a2=(a1-1)/(a1+1)=-1/2009,得a1=-1004/1005
a4=(a3-1)/(a3+1)=-2009
a5=(a4-1)/(a4+1)=1005/1004
a6=(a5-1)/(a5+1)=1/2009
a7=(a6-1)/(a6+1)=-1004/1005
...
可得六个一循环.
2008/6=334....4
故a2008=a4=-2009
a3=(a2-1)/(a2+1)=-1005/1004,得a2=-1/2009
a2=(a1-1)/(a1+1)=-1/2009,得a1=-1004/1005
a4=(a3-1)/(a3+1)=-2009
a5=(a4-1)/(a4+1)=1005/1004
a6=(a5-1)/(a5+1)=1/2009
a7=(a6-1)/(a6+1)=-1004/1005
...
可得六个一循环.
2008/6=334....4
故a2008=a4=-2009
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