算术平方根有意义,an≥0
n≥2时,
x=√an,y=√a(n-1)代入x-y=√6
√an-√a(n-1)=√6,为定值
a1=6 √a1=√6,数列{√an}是以√6为首项,√6为公差的等差数列
√an=√6+√6(n-1)=√6n
an=(√6n)²=6n²
an/[n³(n+1)]=6n²/[n³(n+1)]=6/[n(n+1)]=6[1/n -1/(n+1)]
Sn=6[1/1-1/2+1/2-1/3+...+1/n -1/(n+1)]
=6[1- 1/(n+1)]
=6n/(n+1)