Question

已知数列{an}满足a(n+1)/an=(n+2)/n（n为正整数）,a1=1,则an=?

Answer 1

an = n(n+1)/2

数学归纳即可

an = an/a(n-1) * a(n-1)/a(n-2) * .a3/a2 * a2/a1 * a1

= (n+1)/(n-1) * n/(n-2) * (n-1)/(n-3) * ...4/2 * 3/1 * 1

= (n+1)*n / 2 (中间的都消掉了)