I need to prove or to contradict this claim :
"If a sequence (a_n) converges to a finite limit and a_n != 0 for each n , then the limit of |a_(n+1)|/|a_n| as n->inf is smaller or equal to 1 , i.e
I think that this claim is true . if a_n converges to a limit L, then of course a_(n+1) converges to L as well. Therefore, if L is not 0 , then lim(|a_(n+1)|/|a_n|) = |L|/|L| = 1
The problem here is what if L is to prove this claim is L is 0.
I think it should be done through the definition of a limit of a sequence.
I tried to play with that a little , but I didn't manage to prove that.
Any clues ?
Thanks in advance.!