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,...
Find the original generating function in closed form for (1,2,3,4,5,...).
1 answer