Q17a

Express $T(n)$ in terms of the harmonic number $\displaystyle H_{n}= \sum_{i=1}^{n} \frac{1}{i},\quad n \geq 1$, where $T(n)$ satisfies the recurrence relation, $T(n)=\frac{n+1}{n} T(n - 1)+1$, for $n \geq \sum$ and $T(1) = 1$ What is the asymptotic behaviour of $T(n)$ as a function of $n$ ?