Question

1 A sequence cannot converge to two different limits​

Answer 1

Answer:

it means that L1 − L2 = 0 ⇒ L1 = L2, and hence the sequence cannot have two different limits. . For this ϵ, since an converges to L1, we have that there exists an index N1 so that |an −L1| < ϵ for n>N1. At the same time, an converges to L2, and so there is an index N2 so that |an −L2| < ϵ for n>N2.