Question 13
Consider the following finite sequence of numbers: $\sqrt1,\sqrt2,\sqrt3,\ldots,\sqrt{2023},\sqrt{2024}$. Now, at each turn, select two numbers, say $x$ and $y$, from the sequence which are to be removed and then replace them in the sequence by a single number:
$$z=\sqrt{\frac{1}{\frac1{x^2}+\frac1{y^2}+\frac1{x^2y^2}}}.$$
After doing this 2023 times, a single number is left. What is this number?
Section B instruction: Show your detailed solution.
$$z=\sqrt{\frac{1}{\frac1{x^2}+\frac1{y^2}+\frac1{x^2y^2}}}.$$
After doing this 2023 times, a single number is left. What is this number?
Section B instruction: Show your detailed solution.