如果数列{an}满足a1=2,a2=1且(a(n-1)-an)/(ana(n-1))=(an-a(n+1))/(ana(n+1))(n>=2),如果数列{an}满足a1=2,a2=1且(a(n-1)-an)/(an*a(n-1))=(an-a(n+1))/(an*a(n+1))(n>=2),求a10,(n-1)为下标,请写出过程.

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如果数列{an}满足a1=2,a2=1且(a(n-1)-an)/(ana(n-1))=(an-a(n+1))/(ana(n+1))(n>=2),如果数列{an}满足a1=2,a2=1且(a(n-1)-an)/(an*a(n-1))=(an-a(n+1))/(an*a(n+1))(n>=2),求a10,(n-1)为下标,请写出过程.
如果数列{an}满足a1=2,a2=1且(a(n-1)-an)/(ana(n-1))=(an-a(n+1))/(ana(n+1))(n>=2),
如果数列{an}满足a1=2,a2=1且(a(n-1)-an)/(an*a(n-1))=(an-a(n+1))/(an*a(n+1))(n>=2),求a10,(n-1)为下标,请写出过程.

如果数列{an}满足a1=2,a2=1且(a(n-1)-an)/(ana(n-1))=(an-a(n+1))/(ana(n+1))(n>=2),如果数列{an}满足a1=2,a2=1且(a(n-1)-an)/(an*a(n-1))=(an-a(n+1))/(an*a(n+1))(n>=2),求a10,(n-1)为下标,请写出过程.
原式(a(n-1)-an)/(an*a(n-1))=(an-a(n+1))/(an*a(n+1)) 可以化简为 1/an -1/a(n-1) =1/a(n+1) -1/an 所以得 2/an=1/a(n-1) +1/a(n+1) 所以1/an 就是 1/a(n-1)和 1/a(n+1)的等差中项 所以{1/an} 就是等差数列 因为1/a1 =1/2 1/a2=1 所以公差d=1/a2 -1/a1 =1/2 所以1/a10 =1/a1 +(10-1)d =5 所以a10=1/5

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