Find the generating function of the given sequence: 1, 2, 1, 0, 0
Question
Find the generating function of the given sequence: 1, 2, 1, 0, 0
Solution
The generating function of a sequence is a formal power series in one variable, usually denoted by x, whose coefficients correspond to the terms of the sequence.
The sequence given is 1, 2, 1, 0, 0.
The generating function G(x) of this sequence is given by:
G(x) = 1x^0 + 2x^1 + 1x^2 + 0x^3 + 0*x^4
Simplifying this, we get:
G(x) = 1 + 2x + x^2
So, the generating function of the sequence 1, 2, 1, 0, 0 is G(x) = 1 + 2x + x^2.
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