# Sequence and Cauchy sequence - repost

This project received **10** bids from talented freelancers with an average bid price of **$429 USD**.

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. I need to get this done in 3 hours.. i am attaching the notes as well.. is there anyone who can help? I will pay 20 dollar for all. i am attaching the notes and the question as well. I GIVE HIGH RATE. If you can do few of them, please ask me ..im online and we can negotiate

1)Find a sequence of real numbers {a_i} such that lim┬(n→∞) a_n does not exist , but it has 3 subsequential limits of 0,1,2.

2) Assume {p_n}, and {r_n} are Cauchy sequences in ℝ . Using the definition of a Cauchy sequence prove that {p_n+r_n} is a Cauchy sequence in ℝ.

3) Prove that {1/n^2 } is a Cauchy sequence in ℝ.

4) Assume {p_n}, and {r_n} are Cauchy sequences in ℝ . Using the definition of a Cauchy sequence prove that {p_n+r_n} is a Cauchy sequence in ℝ.

5). Suppose that {a_i} is a Cauchy sequence in a metric space X,d and lim┬(n→∞) a_n=p. Suppose, in addition, {b_i} is a sequence such that d(a_n,b_n)

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