Question 35
Let $(a_n)_{n \ge 1}$ and $(b_n)_{n \ge 1}$ be the sequences defined by the equations
$$
\prod_{k=1}^{n} (2k^2 + i) = a_n + ib_n, \quad n = 1, 2, \dots
$$
Prove that the sequence $\left(\frac{a_n}{b_n}\right)_{n \ge 1}$ is convergent and find its limit.
$$
\prod_{k=1}^{n} (2k^2 + i) = a_n + ib_n, \quad n = 1, 2, \dots
$$
Prove that the sequence $\left(\frac{a_n}{b_n}\right)_{n \ge 1}$ is convergent and find its limit.