Those are both "geometric" sequences:I guess if I understood this it would make sense that as n tends to infinity, the fn. tends to 0.
I am also confused from reading wolfram articles how to evaluate a geometric series and how to tell whether one converges or not. Could someone maybe explain to me how to evalaute:
a) sum between 2&9 of 10^-n
b) sum between 0&ininfity of 3^(-n/2)
And, of course, .
Do you mean the sum? it's fairly easy to see that and that sequence converges to 1 as n goes to infinity.c) determine whether convergent or not:
Between 1&infinity [(n-1)/n]
Do you know this theorem: If converges, then ?
If you you don't recognise that, realize that after n= 100000000000, say, you are still adding numbers close to 1.