用数学归纳法a1=1/2a2=3a1+1=5/2a3=3a2+1=17/2a1+1/2=1a2+1/2=3a3+1/2=9因此先猜想a[n+1]+1/2=3(an+1/2)已证n=2,3时成立假设n=k时成立,即ak+1/2=3(a[k-1]+1/2)当n=k+1时a[k+1]=3ak+1,所以a[k+1]+1/2=3ak+3/2=3(ak+1/...