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

If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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

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If x² - 9x + 18 = 0, what are the roots of the equation?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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

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What is the area of an equilateral triangle with side length 10 cm?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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If a number is divisible by 9, it is also divisible by which of the following?

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What is the value of x if log(x) + log(4) = log(32)?

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