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# Category Archives: USA

## [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. Advertisements

## 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] 2013 AIME I Problem 15

2013 AIME I 15. Let be the number of ordered triples of integers satisfying the conditions (a) , (b) there exist integers , , and , and prime where , (c) divides , , and , and (d) each ordered triple … Continue reading

## 2013 AIME I Problem 15

## [Soln] 2013 AIME I Problem 14

2013 AIME I 14. For , let and so that . Then where and are relatively prime positive integers. Find .

## 2013 AIME I Problem 14

## [Soln] 2013 AIME I Problem 13

2013 AIME I 13. Triangle has side lengths , , . For each positive integer , points and are located on and respectively, creating three similar triangles . The area of the union of all triangles for can be expressed as , where and are relatively prime … Continue reading