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

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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What is the sum of all odd numbers from 1 to 99?

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What is the sum of all even numbers between 1 and 50?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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