Writing that "you are not too good at this" is not justification enough to ask for "all the work" to be done for you, since this is your homework and you must do it, so make and effort, think hard and get contented with some hints:
First, it must be clear that $\displaystyle f(n)>1\,\,\forall\,n\in\mathbb{N}$, so we must check first for which values of n we get $\displaystyle f(n)=1\Longleftrightarrow \sqrt[4]{n}\leq \frac{3}{2}=1.5\,\Longleftrightarrow n\leq \frac{81}{16}\sim 5.06$ $\displaystyle \Longrightarrow\,f(n)=1\,\,for\,\,n=1,2,3,4,5\,,\, \,but\,\,f(6)=2\,\,since\,,\sqrt[4]{6}=1.56>1.5$.
Next, $\displaystyle f(n)=2\Longleftrightarrow\,\sqrt[4]{n}\leq \frac{5}{2}=2.5\,\Longleftrightarrow n\leq \frac{625}{16}\sim 39.06$ $\displaystyle \Longrightarrow f(39)=2\,\,but\,\,f(40)=3\,\,since\,\,\sqrt[4]{40}\sim 2.51$...and etc.
So your sum begins $\displaystyle \sum\limits_{n=1}^1995\frac{1}{f(n)}=5\cdot \frac{1}{1}+24\cdot \frac{1}{2}+...$, since f(n) = 1 for 5 values (n=1,2,3,4,5), f(n) = 2 for 24 values (n= 6,7,...,39), etc.
Now you do the rest following the above method.
Tonio