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