Posted by T.Gracken on October 04, 2002 at 07:43:26:
In Reply to: Caesaro summability: all positive integers sum to -1/12 posted by Adam Getchell on October 04, 2002 at 00:58:21:
: Anyone know how to prove the above? That is,
: (Sum for n = 0 to infinity) n = -1/12
not so. the sum (for n=0 to infinity) of n is infinity [i.e. diverges] and if you think about fundamentals, you can not have a sum less than zero when all of the addends are non-negative.
: I can use Cesaro sums to prove that the harmonic series,
: (Sum for n = 0 to infinity) (-1)^n = 1/2, but I cannot extrapolate to convince myself of the proof above.
the harmonic series is not represented by what you wrote above. the nth term of the sequence is n-1 and the series (from 1 to infinitiy) diverges (...unless you're Dr C)
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