Question

已知等差数列an的公差d＞0,且a4+a6＝10,a4＊a6＝24

Answer 1

公差d＞0,且a4+a6＝10,a4＊a6＝24 所以a4=4,a6=6,公差=(a6-a4)/2=1,

a4=a1+3d

a1=1

an=1+(n-1)d=n

bn=1/(n^2)+1

Tn=(1/1^2+1)+(1/2^2+1)+...+(1/n^2+1)=(1/1^2+1/2^2+...1/n^2)+n

≥[1/(1*2)+1/(2*3)+...+1/(n*(n+1))]+n

=[(1-1/2)+(1/2-1/3)+...+(1/n-1/(n+1))]+n

=1-1/(n+1)+n

所以M的最大值是n+1