Was going over some notes regarding deriving fourier transform equation for Sampling Rate Reduction. Reference to Notes from below link https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-341-discrete-time-signal-processing-fall-2005/lecture-notes/lec05.pdf or from Book Discrete-Time Signal Processing by Alan V. Oppenheim (2nd Edition), equation 4.75.
$$r = i + kM$$
I am lost as to how this is obtained. I understand that every $M-1$ samples are dropped from original sampling results; but still cannot understand how this expression for $r$ is derived.
Could someone help me understand this?