1971 AHSME Problems/Problem 13
Problem
If is evaluated correct to decimal places, then the digit in the fifth decimal place is
Solution
We can rewrite as . By the Binomial Theorem, we know that this expression equals . We are looking for the term (the fifth decimal digit), so we can disregard the first two terms, because they will not affect our final result. Thus, we are left with . The first term here has a term of , and the second term does not contribute to the fifth decimal place, because it does not have enough digits in the numerator. So, we can disregard the subsequent terms, because they will not have enough digits either. Thus, the fifth digit of the expansion is .
See Also
1971 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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