Question

Which of the following series is called the “formal power series”?

(a) b0+b1x+b2x^2+…+bnx^n

(b) b1x+b2x^2+…+bnx^n

(c) 1/2b0+1/3b1x+1/4b2x^2+…+1/nbnx^n

(d) n^2(b0+b1x+b2x^2+…+bnx^n)

I had been asked this question during an interview for a job.

My enquiry is from Discrete Probability topic in chapter Discrete Probability of Discrete Mathematics

Answer 1

Correct option is (a) b0+b1x+b2x^2+…+bnx^n

Easiest explanation: A formal power series is also called a “formal series”, of a field F is an infinite sequence b0, b1, b2, … over F. It is a function from the set of nonnegative integers to F i.e., 0, 1, 2, 3, … → F. A formal power series can also be written as b0+b1x+b2x^2+…+bnx^n.