I encountered a problem which is asks for the first negative term in the expansion of $(1+x)^{\frac{27}{5}}$, where $x$ is always positive,the solution suggested in my module is like this:
$\displaystyle \text{ For the first negative term: } n-r+1 \lt 0 \text{ or, } r \gt 6\frac{2}{5}$, since $n = \frac{27}{5}$
Hence, the 8th term is the first negative term.
But my problem is that I am not getting the rationale behind this approach.Also,if you are aware of any other method for the same problem you may like to post too.
PS:Inquisitive to verify the same using Mathematica,I tried Expand[(1 + x)^(27/5)]
but I guess this is not the correct function.