View the step-by-step solution to:

Question

# Proof. Since xn -> infinity as n ->

infinity , as we can write lim (n -> infinity) xn = infinity.

If for every constant M >0 , there exist no in N such that xn > M for all n > no?????

Solution:
Let lim In+1 En = L. Then, for any e &gt; 0, 3N E N such that for n &gt; N,
Un+1-yn
- I &lt;E=&gt; L-E&lt;
&lt;L+E.
yn+1 - yn
Un+1 - Un
Using that (Un) is a strictly increasing sequence,...

Sines (sin) is unbounded, we can choose 111 large enough so that ym is positive; then we may divide by gm without changing the sides of the inequalities: Sines (yﬂ) is unbounded, taking the limit...

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