true or false,

Question

1) If lim n→∞, an = 0, then Σan is convergent.
2) If lim n→∞, an = 5, then lim n→∞ a n+5 = 5 is convergent.

Answer 1

1) No. Consider the harmonic series
2) ??? if the nth term has a limit, then it converges to that limit.
so a_n+5 also converges to that limit.

Answer 2

So, the first one is false and second one is true?