|Apr14-11, 11:55 PM||#52|
show series [sin(n)]/n converges?
one other technique that would work is an interesting criterion involving the partial sums. let sn be the nth partial sum of the series. If for every epsilon greater than zero there exists an N such that for all n>N we have
|sn+k - sn|<epsilon for all k >= 1, then the series must converge. (Knopp "Theory and Application of Infinite Series") A quick induction on k would make quick work of this series' convergence.
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