Suppose that where series converge conditionally and Help me please in proving following assertion: there exists permutation with properties:
1)
2)
I can prove that for any sequences of positive numbers, such that , there exists a permutation , for which
But I can't apply this properly to initial problem
My question deals nothing with the proof of Riemann's theorem, because the permutation which is built there doesn't satisfy property 1) of mentioned statement. And I don't know whether it is possible to build a permutation with properties 1) and 2) using the method of proof of Riemann's theorem.