已知數(shù)列{an}滿足a1=1,an=a1 +1/2a2 +1/3a3 … +1/(n-1)a(n-1),(n>1,n∈N ),則an的通項公式
a2=a1=1
n>=3時
an+1=a1+1/2a2+.+1/n-1an-1+1/nan
兩式相減得an+1-an=1/nan
即an+1=n+1/nan
即an+1/an=n+1/n
an+1/a2=(an+1/an)(an/an-1).(a3/a2)
=(n+1/n)(n/n-1).(3/2)
=n+1/2
即an+1=n+1/2
即an=n/2
請問求得an+1/an=n+1/n后為什么不能直接用等比數(shù)列公式求an