Hey guys i study for my exams at Wednesday and i would appreciate some help here.

Based on "if for everyε>0, there is $\displaystyle \nu_0\inN$ such that for all natural numbers $\displaystyle m, n > \nu_o$

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1)Prove that the sequence $\displaystyle a_\nu , \nu \in N$ , $\displaystyle a_\nu=\frac{cos1}{1^2}+\frac{cos2}{2^2}+...+\frac{ cos\nu}{\nu}$ is a Cauchy sequence

2) Prove that the sequence $\displaystyle b_\nu , \nu \in N$ , $\displaystyle b_\nu = 1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2\nu-1}$ is not a Cauchy sequence.

Thanks in advance...