1.a,b,c>0,abc=1
prove (inf) 1<1/(1+a)+1/(1+b)+1/(1+c)<2 (sup)
pf:a<=b<=c,a<=1,c>=1,bc>=1,ab<=1
1/(1+a)+1/(1+b)=(1+a+b+1)/(1+a+b+ab)>=1,1<1/(1+a)+1/(1+b)+1/(1+c)
1/(1+b)+1/(1+c)<=1,1/(1+a)<1,1/(1+a)+1/(1+b)+1/(1+c)<2
prove (inf) 1<1/(1+a)+1/(1+b)+1/(1+c)<2 (sup)
pf:a<=b<=c,a<=1,c>=1,bc>=1,ab<=1
1/(1+a)+1/(1+b)=(1+a+b+1)/(1+a+b+ab)>=1,1<1/(1+a)+1/(1+b)+1/(1+c)
1/(1+b)+1/(1+c)<=1,1/(1+a)<1,1/(1+a)+1/(1+b)+1/(1+c)<2
