n=1のとき
(a^(-1)+b^(-1))(a+b)
=((a+b)/(ab))(a+b)
=(a+b)^2/(ab)=1/(ab)=4/sin(72°)^2>4

sin(72°)^2=(1-cos144°)/2
=(1+cos36°)/2
>(1+cos45°)/2
=1/2+(1/4)√2
>0.85
4/sin(72°)^2<4/0.85<5