Topic Details (Notes format)

How to Estimate Factorials Using Stirling’s Approximation

Subject: Mathematics

Book: Maths Mastery

For large n, Stirling’s Approximation n! ≈ √(2πn)(n/e)ⁿ offers a good estimate. For example, 10! = ~3,628,800, while Stirling’s gives ~3,598,700. Although approximate, it’s a vital tool in big data or theoretical analysis where direct factorial computation is cumbersome. Stirling’s bridging helps with limit evaluations, combinatorial growth rates, and advanced probability (like normal approximations to the binomial). Familiarity allows you to handle huge factorials or glean asymptotic insights into complex combinatorial expressions, beneficial in high-level math or algorithmic complexity.

Practice Questions

What is the HCF of 72 and 120?

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If 5x - 2 = 13, what is the value of x?

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What is the sum of all even numbers between 1 and 100?

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What is the greatest common divisor (GCD) of 36 and 48?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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The probability of getting an even number when rolling a die is:

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