Evaluate:
n + n^{2} + n^{3} +... ...+ n^{n}
Limit 
nāā 1^{n} + 2^{n} + 3^{n} +... ...+ n^{n}
I was hoping a numeric approximation would help identify the solution but I couldn't relate what I found with a closed form solution.
I found f(10,000) to be 0.6322235834032078
This was slightly smaller than f(1,000), , suggesting convergence.
The numerator should be:
n * (n^n  1)/(n1)
The denominator should be a polynomial which is one degree more than the numerator, suggesting convergence.
That's as far as I got

def f(n):
num=0
den=0
for i in range(1,n+1):
num += n**i
den += i**n
return num/den
for n in range(1,20):
print(f(n))

Posted by Larry
on 20230527 10:50:01 