00:01
And hello calculus student.
00:03
We're looking at chapter 12, section 4, problem number 26.
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We are given the future value of cash flow as a finite series of n terms, and we're given as f equal c plus c times 1 plus r, plus c times 1 plus r squared, and all the way till c times 1 plus r to the n minus 1.
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So on part a, we're asked to simplify this, basically.
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So what we would do is recognize that we have a sum of n terms.
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So we have a formula for finding the sum of n terms of a geometric series.
00:51
And so we know that that is a...
00:55
Oops, excuse me.
00:57
I got a phone call here.
00:59
Stop that.
01:00
So we have a times r to the n minus 1 over r minus 1.
01:12
So there is our given formula.
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And since we have that a is equal to, so a meaning our first term is equal to c.
01:26
And r, our common ratio to get from one term to the next.
01:30
So we can see we're multiplying by 1 plus r times 1 plus r.
01:33
Right so r our common ratio is 1 plus r and so if we're going to plug in to find our sum of our n terms we can say that f is equal to so a we know is c and then we're multiplying that by r so r we're going to replace with 1 plus r our common ratio and we're going to be n minus 1 and all of that is over r which again is our common ratio of 1 plus r minus 1.
02:17
And if we reduce this down, doesn't have a lot of reducing here.
02:23
Numerator's going to stay the same.
02:26
So 1 plus r in parentheses to the end power minus 1 all over.
02:36
And here the ones are going to cancel and we have r...