Ratio test proof

[member 731016]

Homework Statement

Please see below

Relevant Equations

Please see below

For (a) and (b),

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

Thanks!

 

[nuuskur]

a) b) is standard theory.

Relevant examples also included in the link above.

 

[Office_Shredder]

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 $x_n$?

 

[WWGD]

If the ratio is > 1, then compare to adding a nonzero number to itself " infinitely often", show it will eventually surpass any finite value.