Is the next sum convergence?
1 + 1/2 - 1/3 + 1/4 + 1/5 - 1/6 + 1/7+ 1/8 - 1/9+...
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yes, but conditionally, it's the alternating harmonic series.
The series can be written as... (1)
... where the general term for 'large n' can be approximated as... (2)
... so that the series (1) diverges...
We have ...
The series is thus greater than
Wait a second - if a series does not converge absolutely, is it acceptable to group terms like that?
oh, i misread the problem, i thought the signs were alternated, my bad.
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