Question

已知数列{an}满足a(n+1)/an=n+2/n且a1=1,则an=

Answer 1

a(n+1)/an=n+2/n改成a(n+1)/an=（n+2）/n
这是a(n+1)/an=f(n)的形式，
用累乘法：
a2/a1=3/1
a3/a2=4/2
...
a(n-1)/a(n-2)=n/(n-2)
an/a(n-1)=(n+1)/(n-1)
等式左边相乘=等式右边相乘得
an/a1=n(n+1)/2
an=n(n+1)/2

Answer 2

∵an+1/an=(n+2)/n
∴a2/a1=3/1
a3/a2=4/2
a4/a3=5/3
………
an+1/an=(n+2)/n
∵等式左右相乘相等
∴化简的：an+1/a1=1×1/2×(n+1)×(n+2)=(n+2)(n+1)/2
∵a1=1
∴an+1=(n+2)(n+1)/2
∴an=n(n+1)/2