What's wrong with evaluating at ?
This snag arose out of this post, and these comments by r~~. In that post, I couldn't imagine how
By convention,
for k = 1.
Thus I wrote out the LHS
But r~~ counseled that
I don't know why, but I'm unpersuaded. How does my substitution above differ from evaluating a function at an integer like the following? I can re-word my substitution above, if I define
- James Stewart's Calculus Early Transcendentals (2011 7e), p xxvii, Diagnostic Test C: Functions.
- Ron Larson's Calculus (2018 11e), p 20.
1 answer
The informal expression stands for the formal expression
Now the author of the text obviously wanted to avoid the product notation, either to accomodate those who don't know about the product notation, or alternatively on the assumption that it is more easily understandable that way.
The formal definition of the product (ignoring the special case of the empty product, as it is not relevant here) is:
Let's apply this to the product above:
The author obviously expected the reader to understand this for the case
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