(Solved): b) For each of the following statements, determine if they are true or false. ...

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b) For each of the following statements, determine if they are true or false. Provide justification. (i) If $$\underset{n??}{\lim }{a}_n=0$$, then the series $$?a_n$$ is convergent. (ii) There is a function $$f:\mathbf{R}?\mathbf{R}$$ which is continuous at $$x=0$$ and discontinuous at $$x=1$$. (iii) The function $$g(z)=\frac{\sin z}{z}$$ of the complex variable $$z$$ has a pole at $$z=0$$.