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3. Consider the following property: for any ε>0, there exists N∈N so that whenever n≥N,|u_n+1−u_n|<ε. What...

3. Consider the following property: for any ε>0, there exists N∈N so that whenever n≥N,|u_n+1−u_n|<ε.

    • What is the difference between this property and the definition of a Cauchy sequence?
    • Find a convergent sequence which has this property.
    • Find a divergent sequence which has this property. (Hint: can you think of a function f(x) which grows to infinity very slowly? Then try a_n=f(n).
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