...But I can't get it

We have a sequence of iid nonnegative rv's

Assuming that is finite, we have by the sLLN that converges to a finite limit.

But how can I conclude that ?

I tried to relate it to the series , but the inequality is the other way round than the one that would be helpful...

...so since inequalities don't help me, I hope you guys can help me

Thanks !

Note : I also - miserably - tried Cesàro's mean.