Tag Archives: Algebra

[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

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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.

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[Soln] 2013 AIME I Problem 10

2013 AIME I 10. There are nonzero integers , , , and  such that the complex number  is a zero of the polynomial . For each possible combination of  and , let  be the sum of the zeroes of .Find the sum … Continue reading

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2013 AIME I Problem 10

2013 AIME I 10. There are nonzero integers , , , and  such that the complex number  is a zero of the polynomial . For each possible combination of  and , let  be the sum of the zeroes of .Find the sum … Continue reading

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[Soln] 2013 AIME I Problem 8

2013 AIME I 8. The domain of the function  is a closed interval of length , where  and  are positive integers and . Find the remainder when the smallest possible sum  is divided by 1000.

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2013 AIME I Problem 8

2013 AIME I 8. The domain of the function  is a closed interval of length , where  and  are positive integers and . Find the remainder when the smallest possible sum  is divided by 1000.

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[Soln] 2013 AIME I Problem 5

2013 AIME I 5. The real root of the equation can be written in the form , where , , and  are positive integers. Find .

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