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From: Henryk Trappmann on 27 Jul 2010 03:49
Consider the following polynomial sequence f_n(x):

f_n(x) = -sum from k=1 to n: binomial(n over k)*(-1)^k * (1-x^k)/(1-b^k)

I can show by elementary transformations that
lim_{n -> oo} f_n(b^m) = m for every integer m>=0 and

Does this function sequence converge also for other points x (with
|1-x/b|<1, obtained from numerical tests) than x=b^m and is the limit
log_b(x)?

This function sequence looks too elementary, it must have been
considered already in the history of arithmetics (Euler?). Does it
remind anybody of something?
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