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some of the exercises in this section.6 Just because your answer doesn’t match ours doesn’t mean
it’s wrong. As always, when in doubt, write your answer out. As long as it produces the same
terms in the same order as what the problem wants, your answer is correct.
We would be remiss to close this section without mention of the utility of sequences in everyday
life. Indeed, sequences play a major role in the Mathematics of Finance, as we have already seen
with Equation 6.2 in Section 6.5. Recall that if we invest P dollars at an annual percentage rate r
and compound the interest n times per year, the formula for Ak , the amount in the account after k
5 Here we take ‘experimentation’ to mean a frustrating guess-and-check session.
For more on this, see When Every Answer is Correct: Why Sequences and Number Patterns Fail the Test by
Professor Don White of Kent State University.
6 558 Sequences and the Binomial Theorem
k k −1 r
compounding periods, is Ak = P 1 + n = P 1 + n
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