Binomial series: Lecture 7: Reversing technique in Binomial series (imp)

Binomial series: Lecture 7: Reversing technique in Binomial series (important fundamental) when numbers in multiplication with binomial coefficients are in AP Support the channel:

[krriiiiishd]

The most underrated channel on yt for maths

[VS-]

Respected sir, can you explain how did you replace r with n-r in numerator at 8:32. I knew it was an identity only for Binomial coeff. Wouldn't it establish the relationship n=2r? Edit: in later questions also, the numerators are substituted in a similar fashion.

[talentinvein]

in case of intergals when we substitutes we change the limits accordingly
won't we change limits of summation here???