Math Help Forum - View Single Post - If a (x_n) --> M, then (y_m=(x_1+...+x_m)/m) --> M

Skerven · #3 November 3rd, 2009, 09:21 AM

Quote:

Originally Posted by Plato

If $\varepsilon > 0$ find a $K$ such $n\ge K$ implies that $\frac{{\left| {S_K } \right|}}{n} < \frac{\varepsilon }{2}$

How do you know that you can find such a $K$ ? It seems like you are assuming what you are trying to prove.

Edit: Ok, so you are choosing a K that satisfies the second inequality, justified by assumption.

Then you are increasing K until you find a range of n that satisfied the first inequality. Got it.