如果数列{an}满足a1=2,a2=1,且ana{n-1}/(a{n-1}-a{n})=a{n}a{n+1}/(a{n}-a{n+1}) ,(n>=2) 求a100?先求出an
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如果数列{an}满足a1=2,a2=1,且ana{n-1}/(a{n-1}-a{n})=a{n}a{n+1}/(a{n}-a{n+1}),(n>=2)求a100?先求出an如果数列{an}满足a1=2
如果数列{an}满足a1=2,a2=1,且ana{n-1}/(a{n-1}-a{n})=a{n}a{n+1}/(a{n}-a{n+1}) ,(n>=2) 求a100?先求出an
如果数列{an}满足a1=2,a2=1,且ana{n-1}/(a{n-1}-a{n})=a{n}a{n+1}/(a{n}-a{n+1}) ,(n>=2) 求a100?
先求出an
如果数列{an}满足a1=2,a2=1,且ana{n-1}/(a{n-1}-a{n})=a{n}a{n+1}/(a{n}-a{n+1}) ,(n>=2) 求a100?先求出an
两边取倒数,并约分可得:1/an-1/a{n-1}=1/a{n+1}-1/an
即2×1/an=1/a{n+1} +1/a{n-1}
∴数列{1/an}是等差数列
代入1/a1=½,1/a2=1,可得1/an=½n
∴an=2/n
故a100=1/50
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