Solution to The generating function of the sequence {1,2,3...n..} is (1-z)². - Sikademy
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Archangel Macsika

The generating function of the sequence {1,2,3...n..} is (1-z)².

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No.


We know that


\sum_{n=0}^{\infin} {z^n} =\frac 1 {1-z}


Find derivative of it:


\sum_{n=1}^{\infin} {n*z^{n-1}} =\frac 1 {(1-z)^2}


Change n to n+1


\sum_{n=0}^{\infin} {(n+1)*z^{n}} =\frac 1 {(1-z)^2}


Hence, the generating function of the sequence {1,2,3...n..} is \frac 1 {(1-z)^2}


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