WEBVTT
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let's find the value of C search. That there's
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some over here could not only converges but equals ten
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. So this some over here on the left hand
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side. We can actually rewrite this so that its
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geometric it is geometric, but it might not be
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obvious the way that it's written. So here are
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pull out thiss and here, and the reason you
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can do this is just your laws of exponents.
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So this is geometric with our equals either the sea
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that that's the thing that's being raised to the end
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power and this thing won't converse for all C but
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will converse for some sea because here absolute value are
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it's either the scene and you could just write that
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. Is this because either the exes always positive,
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so you don't have to worry about a negative sign
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? You said that to be less than one,
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because that's when geometric series convergence converges. If absolute
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value bars less than one and here you can solve
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this for seed by just taking the natural log on
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both sides, so seize less than zero. Then
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the Siri's will convert. But that's not enough because
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we want to know also when the sum equals ten
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. So assuming that sees less than zero, we
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know that the sum of the two geometric series.
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So this assumes that emerges, so sees less than
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zero. Then this will equal the first term of
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the series that you get by plugging in and equal
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zero over one minus R seasonings on this case,
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the first term plugging an equal zero and you get
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even the zero, which is one come on,
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one minus r, which is either the sea and
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we want this to be equals a ten on one
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hand. This is the sum of the Siri's because
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she a metric that's where the fractions coming from on
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the left side. On the other hand, we
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wantto find see such that this equals ten. So
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that's why we set the tent on the really inside
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. So all we're going to do now is go
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to the next page here and just solve this new
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equation, Percy. And that will be our final
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answer. One over one minus. Either the sea
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equals ten. This is equivalent. You could just
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float both sides here one minus e to the C
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equals one over his head. simplify this that's nine
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over ten equals either the sea and then I would
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just take lot on both sides. And that's our
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final answer. And also here we can see that
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this number C is a negative number, and that
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was a requirement for C C ten organ to converge
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. This see how to be less than zero.
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And so there actually is a sea value less than
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zero, and it's natural log of nine over ten
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, and that's our final answer.