1983 AHSME Problems/Problem 16
Problem
Let , where the digits are obtained by writing the integers through in order. The ^{rd} digit to the right of the decimal point is
Solution
We consider the first digits, letting the ^{rd} digit be . We can break the string of digits into three segments: let denote (the -digit numbers), let denote (the -digit numbers), and let denote (the -digit numbers). Clearly there are digits in ; in , there are numbers, so digits. This leaves digits in . Notice that with no remainder, so consists of precisely the first -digit numbers. Since the first -digit number is , the ^{th} is , so as is the last digit, the answer is .
See Also
1983 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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