Question

What is the generating function for generating series 1, 2, 3, 4, 5,… ?

(a) \(\frac{2}{(1-3x)}\)

(b) \(\frac{1}{(1+x)}\)

(c) \(\frac{1}{(1−x)^2}\)

(d) \(\frac{1}{(1-x2)}\)

This question was posed to me during an interview for a job.

My enquiry is from Discrete Probability in portion Discrete Probability of Discrete Mathematics

Answer 1

The correct choice is (c) \(\frac{1}{(1−x)^2}\)

To explain: Basic generating function is \(\frac{1}{1-x}\). If we differentiate term by term in the power series, we get (1 + x + x^2 + x^3 +⋯)′ = 1 + 2x + 3x^2 + 4x^3 +⋯ which is the generating series for 1, 2, 3, 4,….

Answer 2

C option is correct