Question: Give a counter example to show that each of the following statement is false:

1. If the general term \({{a}_{n}}\) tends to zero, then \(\sum\limits_{n=0}^{\infty }{{{a}_{n}}}\) converges.
2. \(\sum\limits_{n=0}^{\infty }{c\left( {{a}_{n}} \right)}=c\sum\limits_{n=0}^{\infty }{{{a}_{n}}}\) for a constant \(c\), when \(\sum\limits_{n=0}^{\infty }{{{a}_{n}}}\) does not converge.
3. \(\sum\limits_{n=0}^{\infty }{\left( {{a}_{n}}+{{b}_{n}} \right)}=\sum\limits_{n=0}^{\infty }{{{a}_{n}}}+\sum\limits_{n=0}^{\infty }{{{b}_{n}}}\) when \(\sum\limits_{n=0}^{\infty }{{{a}_{n}}}\) and \(\sum\limits_{n=0}^{\infty }{{{b}_{n}}}\) do not converge.

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