数列an满足a1=1,an+1=2(n+1)方*an/an+2n方,数列2n方/an为等差数列,求数列an的通项公式.

问题描述:

数列an满足a1=1,an+1=2(n+1)方*an/an+2n方,数列2n方/an为等差数列,求数列an的通项公式.

an+1=2(n+1)^2*an/(an+2n^2)右边分子分母同时除以anan+1=2(n+1)^2/(1+2n^2/an)然后将右面的分母乘到左面,左面的式子除到右面1+2n^2/an=2(n+1)^2/(an+1)已知2n^2/an是等差数列,由上式可以知道公差为1,又知道a1=1,所以...