Re: Convergence/Divergence
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<= lim (1/(2n)*1*1*...*1*1 = 0. Of course 0 <= lim (1*3*5*...*(2n-3)*(2n-1))/(2n)^n, so by the Squeeze Theorem lim (1*3*5*...*(2n-3)*(2n-1))/(2n)^n = 0. Make sense?
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I'm having somewhat of a tough time understanding this part of your post. Why is it now 1/2n X 1 X 1 X 1? And what does <= mean?
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<= means "less than or equal to." If we want to use the Squeeze Theorem, we need to find something that is greater than or equal to the limit in question. We can do that by replacing factors in the limit with larger factors. Each of the fractions in the limit is less than 1, so by replacing most of them with 1, we get something bigger. For something simpler, consider that 1/6 = (1/2)*(1/3) <= (1/2)*1 = 1/2. We replaced 1/3 with something larger (namely 1) in order to make the comparison.
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