Question

Sequences ,

Say that I am asked to find whether or not a geometric sequence converges .. I would normally go on and use the ratio < 1 rule .. is there a way to check for convergence by taking somekind of a limit ?

Answer 1

example ⅓ , -1/9 ,1/27 , -1/81, ....

Answer 2

if \(|r|<1\) then \(\displaystyle\lim_{n\to\infty}ar^n=0\)

Answer 3

so does that mean that the sequence converges to zero ? @Zarkon