Ratio test proof

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    Proof Ratio Test
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Homework Statement
Please see below
Relevant Equations
Please see below
For (a) and (b),
1716794684518.png

Does someone please know how to prove this? I don't have any ideas where to start.

Thanks!
 
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a) b) is standard theory.

Relevant examples also included in the link above.
 
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A good starting point is to compare it to a geometric series. For example if ##c=1/3## can you think of a series that converges whose terms are eventually guaranteed to be larger than the ##x_n##?
 
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If the ratio is > 1, then compare to adding a nonzero number to itself " infinitely often", show it will eventually surpass any finite value.
 
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