Series

We are given the series: First, observe the pattern in the denominators. The terms in the denominators follow a sequence of the form: This suggests that the general form of the denominator for the -th term is: Thus, the -th term of the series can be written as: Step 1: The sum of the series up to terms is: This simplifies to:
Step 2: The general formula for the sum of this series up to terms is: Thus, the sum of the series is .