Solution
= Solution
Using the mean $1/p$ of a <geometric distribution> and the decomposition in part (ii),
$$
\boxed{\mathbb E(T_n)
=\sum_{j=1}^n\frac{n}{j}
=n\sum_{j=1}^n\frac1j
=nH_n}.
$$
= Solution
Using the mean $1/p$ of a <geometric distribution> and the decomposition in part (ii),
$$
\boxed{\mathbb E(T_n)
=\sum_{j=1}^n\frac{n}{j}
=n\sum_{j=1}^n\frac1j
=nH_n}.
$$