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Tag Archives: Sequences
[Soln] 2016 Putnam Problem B1
2016 Putnam B1. Let be the sequence such that and for , (as usual, the function is the natural logarithm. Show that the infinite series converges and find its sum.
2016 Putnam Problem B1
2016 Putnam B1. Let be the sequence such that and for , (as usual, the function is the natural logarithm. Show that the infinite series converges and find its sum.
[Soln] 2015 IMC Day 1 Problem 3
2015 IMC 1.3. Let , , and for . Determine whether or not is a rational number.
2015 IMC Day 1 Problem 3
2015 IMC 1.3. Let , , and for . Determine whether or not is a rational number.
[Soln] Problem-Solving Strategies Ch 9 Problem 25
Engel 9.25. The sequence is defined by , . Find the integer part of the sum Note: This problem was taken from Arthur Engel’s Problem-Solving Strategies.
Problem-Solving Strategies Ch 9 Problem 25
Engel 9.25. The sequence is defined by , . Find the integer part of the sum Note: This problem was taken from Arthur Engel’s Problem-Solving Strategies.
[Soln] 2016 AIME I Problem 10
2016 AIME I 10. A strictly increasing sequence of positive integers has the property that for every positive integer , the subsequence is geometric and the subsequence is arithmetic. Suppose that . Find .
2016 AIME I Problem 10
2016 AIME I 10. A strictly increasing sequence of positive integers has the property that for every positive integer , the subsequence is geometric and the subsequence is arithmetic. Suppose that . Find .
[Soln] 2013 Putnam Problem B1
2013 Putnam B1. For positive integers , let the numbers be determined by the rules , , and . Find the value of
Beyond Solutions 
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