已知数列{an}满足a1=2,an+1-an=an+1*an,那么a31等于
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已知数列{an}满足a1=2,an+1-an=an+1*an,那么a31等于
已知数列{an}满足a1=2,an+1-an=an+1*an,那么a31等于
已知数列{an}满足a1=2,an+1-an=an+1*an,那么a31等于
两边同除an*an+1得:1/an-1/an+1=1
1/an+1-1/an=-1,所以数列{1/an}为等差数列
1/an=1/a1+(-1)*(n-1)
1/a31=1/2+(-1)*30
1/a31=-59/2
a31=-2/59
楼主您好:
由于an+1-an=an+1*an
则an+1=an/(1-an)
可得an+2=an/(1-2an)
同理可推得an+3=an/(1-3an)
则an+30=an/(1-30an)
当n=1时,a31=a1/(1-30a1)=-2/59
祝楼主学习进步
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