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$\text{Find the generating function for the following finite sequences} \\1. \ \ \ \ 1, 1, 1, 1, 1, 1,......$
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Assume the generating function

$f(x)=a_0+a_1x+a_2 x^2+a_3 x^3+……$

But, the given sequence is {1, 1, 1, 1, 1…………………}. Using this sequence, the expression above becomes

f(x)$=1 +x+x^2+x^3+…… \\ =(1-x)^{-1}$

Accordingly, $f(x) = (1-x)^{-1}$ is the generating function for the given sequence {1, 1, 1, 1, 1…………………}

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