Question

已知数列{an}满足a1=1,na小n+1=(n+1)a小n+cn(n+1)(c为常数) (1)证明：{a小n/n}是等

Answer 1

a(2)=2+2c

a(3)=3+6c

a(n)=n[1+(n-1)c]

a(k)=k[1+(k-1)c]

ka(k+1)=(k+1)a(k)+ck(k+1)=(k+1)k(1+kc)

a(k+1)=(k+1)(1+kc)

a(n)/n=1+(n-1)c

p[1+(p-1)c]=q[1+(q-1)c]

c=(q-p)/[(q-p)(1-q-p)]=1/(1-q-p)