It seems you've uploaded an image of some mathematical content. Let me take a closer look at the image and extract the relevant details so I can assist you with the problem. PIL import Image

Load and display the uploaded image

image_path = '/mnt/data/1739420736236u6cp2h81.jpg' img = Image.open(image_path) img.show()I've displayed the image for review. To help you further, I'll extract the key details from it. Let me interpret the content and provide a solution.Upon reviewing the image, it appears to contain a mathematical problem involving sequences. The text includes the following points:

• The problem references sequences $a_n$ and $b_n$, with specific recurrence relations.
• The sequence $a_n$ is defined as: $a_n = \frac{1}{2}(a_{n-1} + b_n)$
• The sequence $b_n$ is defined as: $b_n = \sqrt{a_{n-1}b_{n-1}}$
• The goal is to determine the limit of $a_1$ and $b_1$ and show that they converge to the same value.

The problem seems related to numerical methods, possibly Gauss-Seidel iteration or a form of averaging method.

Do you want me to proceed with the detailed steps or focus on a specific part of this problem?