Which is correct? Proving - numerical analysis (separation of symbols)

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The discussion centers on the mathematical proof involving the function f(x+n) and its representation through recursive relationships. Two formulations are presented, questioning their equivalence without the inclusion of binomial coefficients. The participants highlight the necessity of these coefficients for accurate representation, particularly when expanding (1+/\)^n. The consensus indicates that the absence of binomial coefficients renders the two expressions non-equivalent.

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Proving - numerical analysis (separation of symbols)

How do I prove this?

f(x+n) = f(x+n-1) + /\f(x+n-2) + ... + /\^(n-2) f(x+1) + /\^(n-1) f(x) +
/\^n f(x-1)
 
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irony of truth said:
Which of these must be true?

f(x+n) = f(x+n-1) + /\f(x+n-2) + ... + /\^(n-2) f(x+1) + /\^(n-1) f(x) +
/\^n f(x-1),

OR

f(x+n) = f(x+n-1) + /\f(x+n-2) + ... + /\^(n-2) f(x+1) + /\^(n-1) f(x) +
/\^n f(x)


?

This was the question given in my homework... I just doubt it because my
professor could have miswritten our assignment.

I stumbled upon this problem as well... i can't really see how these two are equivalent without their corresponding binomial coefficients when f(x+n) = E^n f(x) = (1+/\)^n f(x) and (1+/\ )^n is expanded ^^;
 

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