解:a1-2×1/2=1,则a1=2
n*a[n+1]-(n+1)*a[n]=2
即a[n+1]/饥银运(n+1)-a[n]/n=2/n(n+1)=2/n-2/(n+1)
即烂梁a[n+1]/(n+1)+2/(n+1)=a[n]/n+2/n
即(a[n+1]+2)/(n+1)=(a[n]+2)/n
设b[n]=(a[n]+2)/n,则由上式可知:b[n+1]=b[n]
即b[20]=b[19]=b[18]=...=b[1]=(a[1]+2)/1=4
即搏改(a[20]+2)/20=4
即a[20]=78