设a1=1,an+1+=0,证明:数列{an}收敛,并求an.

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问题 设a1=1,an+1+=0,证明:数列{an}收敛,并求an

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答案先证明{an}单调减少, a2=0,a2<a1; 设ak+1<ak,ak+2=[*],由ak+1<ak得1一ak+1>1一ak, [*]

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