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

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In summary, the conversation discusses proving a numerical analysis problem involving the separation of symbols. The question is whether f(x+n) can be represented as two different equations involving binomial coefficients. The speakers have doubts about the validity of the problem.
  • #1
irony of truth
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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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  • #2
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 ^^;
 
  • #3
+ ... + /\^(2n-3) f(x-n+2) + /\^(2n-2) f(x-n+1)

Both statements are correct and refer to the same concept. Proving in numerical analysis involves breaking down a mathematical problem into individual symbols or components to analyze and verify its accuracy. This approach allows for a more systematic and rigorous method of proving mathematical equations and theories. To prove the equation provided, one would need to use mathematical techniques and principles to manipulate the symbols and demonstrate that both sides of the equation are equivalent. This process may involve using algebraic manipulations, calculus, or other mathematical tools. Ultimately, the goal is to show that the equation holds true for all values of x and n, thus providing evidence for its validity.
 

1. What is the difference between "which" and "that"?

The words "which" and "that" are both relative pronouns used to introduce a subordinate clause in a sentence. "Which" is used when the information following it is non-essential to the meaning of the main clause, while "that" is used when the information is essential to the meaning of the main clause.

2. Can "which" be used to refer to people?

Yes, "which" can be used to refer to people. However, it is more commonly used to refer to things or animals. When referring to people, "who" is a more appropriate pronoun to use.

3. Is "which" always used for singular nouns and "which" for plural nouns?

No, this is not always the case. "Which" can be used for both singular and plural nouns. It depends on the context and the meaning of the sentence.

4. How do I know when to use "which" or "what" in a question?

"Which" is used to ask for a specific choice or selection, while "what" is used to ask for general information or an explanation. For example, "Which color do you prefer?" vs "What is your favorite color?"

5. Can "which" be used as a subject in a sentence?

Yes, "which" can be used as a subject in a sentence. It is often used in a sentence to introduce a relative clause that provides more information about the subject. For example, "The book, which I bought yesterday, is now on the bestseller list."

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