Question: Let {a_n} be a sequence of rational numbers defined as follows:
a_1 = 1
a_(n+1)=a_n + 1/(3^n)
for all n
> 1.
1) Show that {a_n} is a Cauchy sequence and hence convergent
2) Find it's limit.
So.. I am a bit lost for this one.
I tried using induction to bound a_n by 1 and 2, but I couldn't bound it above. I figured if I bound it above, and prove that it's a non-decreasing function, then I could prove that it converges, and thus that it is Cauchy...
Any tips for me to get started on this? Thanks!