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Homework Statement
[itex]\sum[/itex][itex]^{∞}_{1}[/itex]1/n[itex]^{n}[/itex]
Homework Equations
Direct comparison testThe Attempt at a Solution
Since the main factor in the equation is the exponent that would be changing as n goes to infinity, I know that from the p series as p > 1 the the series converges. So I know that I would be comparing the original equation to[itex]\sum[/itex][itex]^{∞}_{1}[/itex]1/n[itex]^{2}[/itex]
And I know that I need to show:
0 [itex]\leq[/itex] [itex]\sum[/itex][itex]^{∞}_{1}[/itex]1/n[itex]^{n}[/itex] [itex]\leq[/itex] [itex]\sum[/itex][itex]^{∞}_{1}[/itex]1/n[itex]^{2}[/itex]
but I don't know how to show
[itex]\sum[/itex][itex]^{∞}_{1}[/itex]1/n[itex]^{n}[/itex] [itex]\leq[/itex] [itex]\sum[/itex][itex]^{∞}_{1}[/itex]1/n[itex]^{2}[/itex]
mathematically. Would I just blatantly say that the original term is smaller than the p series just by looking at it?