Question

Lim n->infinity of (2+(-1)^n)

Answer 1

limit D.N.E. because the (-1)^n oscillates between negative and positive numbers.

Answer 2

Challenge them with \(\epsilon=0.5\).
Since \(1-(-1)=2\), there is no \(N\) such that \(n>N\implies |a_n-L|<0.5\).