i equally thanked everybody once! (Happy) PaulRS' solution is nice and my solution differs from his in the last setp only, where i applied Cesaro's mean, as Moo mentioned, to the sequence

that will give you and thus

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- June 11th 2009, 01:24 PMNonCommAlg
i equally thanked everybody once! (Happy) PaulRS' solution is nice and my solution differs from his in the last setp only, where i applied Cesaro's mean, as Moo mentioned, to the sequence

that will give you and thus - August 7th 2009, 04:19 AMluobo
Define , then

If exists, it implies:

(1)

(2) Series , converges, since .

The first term converges since it is . The second term is .

For the second term to converge, it requires , so , noting . This also confirms does exist.