\begin{align} T(0) & = 0 \\ T(n) & = T(n-1) + \dfrac{1}{n} \end{align} solve the recurrence relation
My work so far:
\begin{align} T(1) & = 1 \\ T(2) & = 1 + \dfrac{1}{2} \\ T(3) & = 1 + \dfrac{1}{2} + \dfrac{1}{3} \\ &\vdots \end{align}
this is the harmonic series, which diverges.
What is the solution to the recurrence relation?