数列an满足a1=1且an+1/an=n+2/n,当大于等于2时,an=?

Question

数列an满足a1=1 且an+1/an=n+2/n,当大于等于2时,an=?

Answer 1

根据题意有
an/an-1=n+1/n-1
an-1/an-2=n/n-2
...
a2/a1=3/1
左边全部相乘得到an/a1=（n+1）n（n-1）...*4*3/1*2*3*4...*（n-1）=（n+1）n/2
所以an=n（n+2）/2