Re: show that sum(1/(1+exp(n*x)), n=0..infinity) is uniform convergent

Scoobidoo vient de nous annoncer :
how do I show that sum(1/(1+exp(n*x)),n=0..infinity) is uniform convergent?

For x in [a, infty[,
exp(n*x) >= exp(n*a), so :
| 1/(1+exp(n*x) | =< 1/exp(a*n)
=< ( 1/exp(a) )^n
Since a>0, | 1/exp(a) | < 1,
and so the gometric series sum( (1/exp(a) )^n ) converges, what proves that your series is normally convergent.


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