高二数列问题对于正数p1,p2,...,pn（n为正整数）,我们称n/（1/p1+1/p2+...21/pn）为它们的调

an=n(n+1)/(2n+1)=n/(1/b1+1/b2+...+1/bn)
n/an=(2n+1)/(n+1)=1/b1+1/b2+...+1/bn
1/b1=3/2
1/bn=(2n+1)/(n+1)-(2(n-1)+1)/n
=((2n+1)n-(2n-1)(n+1))/n(n+1)
=1/n(n+1)
bn=n(n+1) (n>=2)
所以bn=2/3 (n=1)
n(n+1) (n>=2)
a1^2/b1
=2/3
(an)^2/bn
=n(n+1)/(2n+1)^2
=0.25(4n^2+4n+1-1)/(4n^2+4n+1)
=0.25-0.25/(4n^2+4n+1)
当n=1时最大,最大值为2/3
当n为无穷大时最小,最小值为0.25