Question

What sequence is represented by the generating function obtained by taking the derivative of the generating function of the even numbers {0, 2, 4, 6, ...} ? (write the first five numbers)

Answer 1

The generating function seems to be 2n. The derivative of which is just 2, so is a constant function.

Answer 2

Wrong.

Answer 3

Ok.

Answer 4

A poorly-phrased question. Did you write it word for word?

Answer 5

Yes..

Answer 6

It seems properly phrased to me. I provided a clue to the right answer, but Entei is not interested in the right answer, I see.

Answer 7

May be I should say, I don't understand what the question is asking.

Answer 8

ITs not right though...

Answer 9

The question is asking for the first five terms of a generating function that is derived from a function which outputs even numbers.
The function which outputs even numbers is y=2n, nε{0,1,2,3,4, ...}
The derivative of that function is y'=2, which outputs (for any n): {2, 2, 2, 2, 2}

Explain to me why it's not right, Entei. You asked the question, and apparently you already know the correct answer.

Answer 10

@CliffSedge - I believe @Entei might be referring to this when he talks about "generating function": http://mathworld.wolfram.com/GeneratingFunction.html

If this is correct, then the generating function for even numbers is:\[f(x)=\frac{2x}{(x-1)^2}=2x+4x^2+6x^3+8x^4+...\]see here: http://mathworld.wolfram.com/EvenNumber.html

Answer 11

Then chaguanas was correct that it is not a properly posed question, as it should have asked for the function that generates even coefficients

Answer 12

Maybe Entei used the term "generating function" in the context that he /thought/ evryone else new it as.