Question

已知数列{an}中,a1=1，且满足an+1=an+an/(n+1)求通项公式 an+1=an+an/(n+1) (n+1)*a(n+1)=(n+2)*an a(n+1

已知数列{an}中,a1=1，且满足an+1=an+an/(n+1)求通项公式
an+1=an+an/(n+1)
(n+1)*a(n+1)=(n+2)*an
a(n+1)/an=(n+2)/(n+1)做到这一步不知道怎么做了

Answer 1

an+1=an+an/(n+1) (n+1)*a(n+1)=(n+2)*an a(n+1)/an=(n+2)/(n+1) 则: an/a(n-1)=(n+1)/n a(n-1)/a(n-2)=n/(n-1) .................. a2/a1=3/2 所有项相乘,得: an/a1=(n+1)/2 an=(n+1)/2*a1=(n+1)/2 通项公式: an=(n+1)/2

追答

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