Here is a neat problem I did yesterday.
Show that
(Pre-calc students cover your ears)
Then use it to show that
converges
Not too hard if you see it, but neat I think .
trivial
Does not converge for any , since:(Pre-calc students cover your ears)
Then use it to show that
converges
Some numerical evidence:
Code:>k=2:100; >x=2; >s=1/logbase(x,k); > >S100=sum(s) 524.765 > > >k=2:1000; >x=2; >s=1/logbase(x,k); > >S1000=sum(s) 8529.4 > > > >k=2:10000; >x=2; >s=1/logbase(x,k); > >S10000=sum(s) 118458 >
RonL
It is trivial in the sense that it requires routine application of what they should know about change of base for logs and how to add fractions.
You said use the identity to show that the given series converges, well it does not converge, and it obviously does not without recourse to the identity.And yes, it was a trick question
I just said that since it equatls
Then
RonL