i)Prove, by using the formal deﬁnition of limit, that the sequence
(1 + 5n)/n + n i / n + 3 n ∈ N
has limit 5 + ı.
ii)Prove that the fact that the above sequence converges to 5 + i implies that the sequence
square root of ( [(1 + 5n)^2 / n^2] + [n^2 / (n+3)^2] ), n ∈ N
converges to
√26.
Note: In this question you can assume without proof that the inequalities
||z| − |w|| ≤ |z + w| ≤ |z| + |w| hold for all z and w in C

can anyone help me with this example? thanks

Question

i)Prove, by using the formal deﬁnition of limit, that the sequence
(1 + 5n)/n + n i / n + 3  n ∈ N
has limit 5 + ı.
ii)Prove that the fact that the above sequence converges to 5 + i implies that the sequence
square root of (  [(1 + 5n)^2 / n^2] + [n^2 / (n+3)^2] ), n ∈ N
converges to
√26.
Note: In this question you can assume without proof that the inequalities
||z| − |w|| ≤ |z + w| ≤ |z| + |w| hold for all z and w in C

can anyone help me with this example? thanks