Sum of series of fractions I am trying to find the $f$ formula that returns the sum of the series created by fractions that have constant nominator and shifting by one denominator. 
Here are some examples:
$$f(3) = \frac{3}{1} + \frac{3}{2} + \frac{3}{3} = 5.5$$
or
$$f(4) = \frac{4}{1} + \frac{4}{2} + \frac{4}{3} + \frac{4}{4} = 8.33$$
or
$$f(5) = \frac{5}{1} + \frac{5}{2} + \frac{5}{3} + \frac{5}{4} + \frac{5}{5} = 11.4166$$
or
$$f(200) = \frac{200}{1} + \frac{200}{2} + \frac{200}{3} + ... + \frac{200}{200} = 1175.6062$$
Does anyone have an idea on how to calculate the sum of this series?

There is a way to approximate quite well the value 
$$k H_k\approx \frac{1}{2}+k \left(\gamma -\log \frac{1}{k}\right)$$
where $\gamma\approx 0.577216$ is Euler constant and $\log$ are natural logarithms
Here is a table which shows 
$$
\begin{array}{r|r|r}
k & \textit{actual value} & \textit{approximation}\\
\hline
 10 & 29.289683 & 29.298008 \\
 20 & 71.954793 & 71.958959 \\
 30 & 119.84961 & 119.85239 \\
 40 & 171.14172 & 171.14380 \\
 50 & 224.96027 & 224.96193 \\
 60 & 280.79222 & 280.79361 \\
 70 & 338.29857 & 338.29976 \\
 80 & 397.23834 & 397.23938 \\
 90 & 457.43135 & 457.43228 \\
 100 & 518.73775 & 518.73859 \\
\end{array}
$$
