How to simplify this summation to an incomplete gamma function

PureStorm
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Could someone please explain why the following sum simplifies to the following?

Q9bDW.png


=
EUjtg.png


As far as I can see, this sum does not correlate to the formula for incomplete gamma function as a sum. I'd appreciate any help as the incomplete gamma function is somewhat beyond the scope of my current course.



P.S. I managed to do it eventually. The key was recognising that n-k could be substituted for k as k varies from 0 to n.
 
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