Calculating probability for collision Image Taken from Birthday Paradox
Taken from Birthday Paradox
Why when k$<<$m, we can replace (1-$\frac{i}{m}$) with $e^\frac{i}{m}$? I do not understand the calculation steps in the article starting from the seconds step. Can someone explain to me or point out some of the keywords or topics I should explore to find out?

We use the taylor serie of $e^x$ (here $x=-\frac{i}{m}$) to the first order:
\begin{equation}
e^{-\frac{i}{m}}=1-\frac{i}{m} 
\end{equation}
with $i\ll m$
