Answer to Question #148950 in Discrete Mathematics for Surya

Question #148950
The generating function of the sequence {1,2,3...n..} is (1-z)².
1
Expert's answer
2020-12-11T13:08:54-0500

No.


We know that


n=0zn=11z\sum_{n=0}^{\infin} {z^n} =\frac 1 {1-z}


Find derivative of it:


n=1nzn1=1(1z)2\sum_{n=1}^{\infin} {n*z^{n-1}} =\frac 1 {(1-z)^2}


Change n to n+1


n=0(n+1)zn=1(1z)2\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 1(1z)2\frac 1 {(1-z)^2}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment