Sequence involving square roots - Iran First Round 2018, P24
Source: Iran First Round 2018, P24
March 7, 2021
number theoryalgebraSequences
Problem Statement
The sequence {an} is defined as follows: \begin{align*} a_n = \sqrt{1 + \left(1 + \frac 1n \right)^2} + \sqrt{1 + \left(1 - \frac 1n \right)^2}. \end{align*} What is the value of the expression given below? \begin{align*} \frac{4}{a_1} + \frac{4}{a_2} + \dots + \frac{4}{a_{96}}.\end{align*}<spanclass=′latex−bold′>(A)</span>18241<spanclass=′latex−bold′>(B)</span>18625−1<spanclass=′latex−bold′>(C)</span>18625<spanclass=′latex−bold′>(D)</span>19013−1<spanclass=′latex−bold′>(E)</span>19013