Asked by Anonymous
Find the original generating function in closed form for (1,2,3,4,5,...).
Answers
Answered by
Steve
since 1,1,1,1,1... has its function
â
âx^n = 1/(1-x)
n=0
take the derivative
ânx^(n-1) = 1/(1-x)^2
now replace n-1 with n and you have
â(n+1)x^n = 1/(1-x)^2
generates
1,2,3,4,5,...
â
âx^n = 1/(1-x)
n=0
take the derivative
ânx^(n-1) = 1/(1-x)^2
now replace n-1 with n and you have
â(n+1)x^n = 1/(1-x)^2
generates
1,2,3,4,5,...
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