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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

## [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

## [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 .