It is proved that if the limit of sequence xn is a, then for any natural number k, the limit of sequence xn + k is a

It is proved that if the limit of sequence xn is a, then for any natural number k, the limit of sequence xn + k is a

It is proved that LIM xn = a (n tends to infinity)
Let m = n + K, because K is a natural number and M tends to infinity
So Lim XM = a (M tends to infinity), that is Lim x (n + k) = a