WEBVTT
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were given that this sum of am convergence both the
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sum of being diverges and we'LL use this to show
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that the Siri's of A and plus beyond his diversion
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and the hit is that we should argue by contradiction
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. So let's follow the hidden here. So let's
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go ahead and suppose that this sum of a M
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plus B end conversions then if we take this summon
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, subtract this sum. This will also converge because
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we're just subtracting two real numbers here. If this
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some conversions, that means that the sum of a
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and lesbians a real number. Similarly, we're already
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assuming that this son commercials that means the sums of
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real number. So when I subtract, this is
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also a real number. So here, let me
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not say conversions. I'll just say this is a
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real number. However, this Siri's here. We
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can also rewrite this is and plus being minus and
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and then here because we're just dealing with real numbers
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on the inside. Well, you just go ahead
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and cancel those ends. We have the sum of
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bien. So on one hand, this expression here
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, the difference of the two sums is a real
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number on the other hand, this sum is also
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equal to the sum of the end. But we're
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told that this diverges that was the assumptions. So
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it is impossible for the sum of the end to
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be a real number and diverge. It's one or
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the other. If it's equal to a real number
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, that would mean converges. Excuse me. Therefore
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, we've arrived at the contradiction, and that's our
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final answer.