[arahant]

[ QUOTE ]
Show that 1+1/2+1/3+1/4+...1/p - lnp < 1 for all p >1

[/ QUOTE ]

1+1/2+1/3+1/4+...1/p - lnp < 1 for all p >1, QED

I challenge anyone to find a more parsimonious proof.