Question about sum of integer involving factorial notation

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The discussion centers on the mathematical concept of summation involving factorial notation, specifically addressing the importance of the variable 'r' within the summation sign. It is established that removing 'r' from the summation leads to incorrect conclusions, as 'r' is essential for defining the limits of the summation. The proof of the statement can be effectively demonstrated using mathematical induction, confirming the necessity of maintaining 'r' in the expression.

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Sanosuke Sagara
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I have my question and my problem in the attachment that followed.
 

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Damn right you don't know how to continue. That is because you took r out of the sumation sign and you cannot do that because r is the thing that varies in your sumationg sign. r is nothing without the sumation sign!

The proof is easily done by induction.
 

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