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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