Sn = 1 + 1 / 2 + 1 / 3 +. + 1 / N, f (n) = s2n + 1-sn + 1, f (n) > m is constant, the value range of M is constant

Sn = 1 + 1 / 2 + 1 / 3 +. + 1 / N, f (n) = s2n + 1-sn + 1, f (n) > m is constant, the value range of M is constant

S(2n+1)=1+1/2+1/3+.+1/(2n+1)
S(n+1)=1+1/2+1/3+.+1/(n+1)
f(n)=1/(n+2)+1/(n+3)+…… +1/(2n+1)
f(n+1)=1/(n+3)+…… +1/(2n+1)+1/(2n+2)+1/(2n+3)
f(n+1)-f(n)=1/(2n+2)+1/(2n+3)-1/(n+2)
>1/(2n+2)+1/(2n+3)-2/(2n+4)>0
limf(n)=1/(n+2)+1/(n+3)+…… +1/(2n+1)=ln(2n+1)-lnn=ln2
n->∞
m