WEBVTT
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for this problem, we're going to recall the fact
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that you, the exes one plus X plus x
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squared over two factorial plus X cubed over three factorial
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plus dot, dot dot and in the swearing of
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four is two. He is a number that's less
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than four. So the square root of E should
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be a number that's less than two. Therefore,
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this sum should be something that's bigger than the end
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through of the square root of E. In other
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words, the end through tiv e to the one
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half. No, another way of writing This is
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E to the one over two n. And now
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we can use this expansion up here on this,
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either one over to N to get any calls.
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One to infinity, one plus one over to end
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. Plus, I'm just going to put dot,
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dot, dot For these other terms, we started
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this minus one. So this one and this minus
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one will cancel these dot, dot, dot terms
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. The ones that we see here, they're going
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to be something that's positive. So whatever they are
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, we know that we're going to get more when
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we had them on. So this left hand side
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should be bigger than some from in equals, one
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to infinity of just one over to N. And
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this is just the harmonic. Siri's divided by two
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. So infinity, divided by two, is still
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infinity, so we will still get divergent.