infinite seq., series: If S{an} converges, then S{1/an}....

[maeveoneill]

can someone help me get started with this question.. or suggest what i would have to do.

Q. suppose that

infin
__
\ an (an cannot = 0)
/
---
n=1

is known to be a convergent series. Prove that

infin
__
\ 1/an
/
---
n=1

is a divergent series.

 

[pka]

If the series \(\displaystyle \sum {a_n }\) converges then you know that the sequence \(\displaystyle \left( {a_n } \right) \to 0\)?
What does that tell you about the sequence \(\displaystyle \L \left( {\frac{1}{{a_n }}} \right)\)?
Now answer the question.