Simplify the following sum $sum_{i=1}^nfrac1{n-(i-1)}$

Extremely simple question, but one I am struggling with (I haven’t taken a math class for a couple years so this may be very easy).
I just need to simplify the following sum, but can’t seem to figure out how:

$sum_{i=1}^nfrac1{n-(i-1)}$

I am really struggling to find where to start, since it seems you would need to break the sum into parts to simplify, but I don’t think you can. My best guess would be doing something like below, but I don’t think you can break the fraction into parts like this (but can’t think of any other way to solve)

$sum_{i=1}^nfrac1{n-(i-1)} =sum_{i=1}^nfrac1{n} – sum_{i=1}^nfrac1{i} – sum_{i=1}^n1 = 1 – H_n – n$

I have also heard from a semi-reliable force that this equals $H_n$ but not sure if this is right/how it was reached.