Demonstrate that the limit from these successions is 0 using the definition
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Steven G
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How do you go from n^2<e to n^2>1/e??
Let n^2=1/2 and e = 6/10.
Then surely 1/2 = .5 < 6/10=.6
However, 1/2 >1/.6?? Since 1/.6 >1, then surely 1/2 < 1/.6
From another angle. Since e>0 can be any value (especially as small as we like), then at some point n^2<1/e, since 1/e -->oo as e-->0.
Let n^2=1/2 and e = 6/10.
Then surely 1/2 = .5 < 6/10=.6
However, 1/2 >1/.6?? Since 1/.6 >1, then surely 1/2 < 1/.6
From another angle. Since e>0 can be any value (especially as small as we like), then at some point n^2<1/e, since 1/e -->oo as e-->0.