i can.. take note that is always positive, therefore if i remove it, the remaining would be strictly less than M..
where is the flaw there? you are the only person i know who disagreed with that.. as far as i'm concerned..
i have explained the reason why that is true..
I think you need some fairly heavy-duty analysis to deal with this.
Let ε > 0. since , there is an integer N such that whenever n≥N. For any positive integer r,
Therefore It follows that as r→∞. Hence for all sufficiently large r. In fact, since as r→∞, we even have for all sufficiently large r. Putting n=N+2r (or n=(N+1)+2r, which works equally well), you see that for all sufficiently large n.
Finally, for all sufficiently large n. Since ε was arbitrary, this shows that as n→∞.