Can someone explain to me why [sin(0.5*npi)]/n converges to 0.
The explanation I have been given is that since it is < 1/n and therefore can be made as small as we like for large enough n.
But I don't follow why it is smaller than 1/n. 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)
c) determine whether convergent or not:
Between 1&infinity [(n-1)/n]