uxor 

I was searching for new exercises on semi-convergent series using the Dirichlet criterion :

Σ a_n b_n converge if a_n->0 and |Σ_a^b b_n| uniformly bounded

Then I found a very hard example :

Σ (-1)^k /(k*exp(sin(k))

the Abel criterion applies with b_k=(-1)^k *exp(-sin(k)) but this requires to study the Fourier series of exp(-sin(x)) and the finiteness of the irrationality mesure of pi* !

* Mahler, K. (1953)

#mathematics

9:16pmWeb
Show threaduxor 4h ago

The example
Σ (-1)^k /(k*exp(sin(k))
is so interesting, I asked wolframalpha about its convergence and it says that the series diverge 😮 A rare example of mistake from wolframalpha !

#mathematics