两边取倒数
1/a(n+1)=1/a(n)+1/3
{1/a(n)}是一个等差数列
1/a(n)=1/a(1)+(n-1)*1/3
解得a(n)=3/(n+5)
a(n)*a(n+1)
=9/(n+5)(n+6)
=9*(1/(n+5)-1/(n+6))
所以s=9(1/6-1/7+1/7-1/8+1/8-.+1/(n+5)-1/(n+6))
=9(1/6-1/(n+6))
=9n/[6*(n+6)]
=3n/[2*(n+6)]
两边取倒数
1/a(n+1)=1/a(n)+1/3
{1/a(n)}是一个等差数列
1/a(n)=1/a(1)+(n-1)*1/3
解得a(n)=3/(n+5)
a(n)*a(n+1)
=9/(n+5)(n+6)
=9*(1/(n+5)-1/(n+6))
所以s=9(1/6-1/7+1/7-1/8+1/8-.+1/(n+5)-1/(n+6))
=9(1/6-1/(n+6))
=9n/[6*(n+6)]
=3n/[2*(n+6)]