https://file.aiquickdraw.com/mathbot/file/17255553820033r912awr.jpg

The equation in the image is:

\[
\lim_{n \to \infty} \left( 1 - \frac{1}{2} \right) \left( 1 - \frac{1}{4} \right) \cdots \left( 1 - \frac{1}{2n} \right)
\]

This represents the limit of a product as \( n \) approaches infinity. The product inside the limit is over terms of the form \( 1 - \frac{1}{2k} \) where \( k \) ranges from 1 to \( n \).

Would you like a detailed solution or have any specific questions about this limit?

### Here are some related questions:
1. How do you evaluate the limit of a product as \( n \) approaches infinity?
2. What is the connection between this type of product and infinite series?
3. How can you approximate this product for large \( n \)?
4. What mathematical tools are typically used to analyze such products?
5. How does this expression relate to known infinite product results?

**Tip:** When dealing with limits that involve products or sums, it’s often useful to take the logarithm to simplify the expression before analyzing the limit.

Evaluate the limit of the product as n approaches infinity: (1 - 1/2)(1 - 1/4) ... (1 - 1/2n).

Explore the evaluation of the limit of an infinite product as n approaches infinity. This detailed solution covers the essential calculus concepts, formulas, and theorems involved in evaluating the product of terms like (1 - 1/2)(1 - 1/4)... (1 - 1/2n). Suitable for undergraduate students.

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