求数列4/3,16/15,36/35,64/63.的前n项和
问题描述：
求数列4/3,16/15,36/35,64/63.的前n项和
答
4/3+16/15+36/35+64/63+.+(4n²)/(2n-1)(2n+1)
=（1+1+.+1）+(1/3+1/3×5+1/5×7+.+1/(2n-1)(2n+1))
=n+1/2*(1-1/3+1/3-1/5+.+1/(2n-1)-1/(2n+1))
=n+1/2*(1-1/(2n+1))
=n+n/(2n+1)
=2n(n+1)/(2n+1)