It is well-known that in average $\varphi(n)$ behaves like $\frac1{\zeta(2)}n=\frac{6}{\pi^2}n$. But it looks that in some sense it is ``asymptotically larger''. In particular, the ratio $$ \zeta(2)(1-t)^2\sum_{n=1}^{\infty} \varphi(n)t^{n-1}= \zeta(2)\frac{\sum_{n=1}^{\infty} \varphi(n)t^{n-1}}{\sum_{n=1}^{\infty} nt^{n-1}} $$ seems to be greater then 1 when $t$ increases to 1 (my caclulations say so), and analogous things appear for other averaging procedures involving $\varphi(n)$.

Does it have some sense and/or explanation?