Find the solution for each of the following recurrences, and then give tight bounds for $T(n).(30$ points$)$

a$.T(n)=T(n-1)+\frac{1}{n}$ with $T(0)=0$

b$.T(n)=T(n-1)+c^n$ with $T(0)=1,$ where $c>1$ is some constant

c$.T(n)=T(n-1)+1$ with $T(0)=1$