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

A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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What is the sum of all angles in a hexagon?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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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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What is the sum of the interior angles of a hexagon?

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What is the probability of drawing a king from a standard deck of 52 playing cards?

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What is the length of the diagonal of a square with a side length of 7 cm?

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What is the area of a circle with a diameter of 14 cm?

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If x^2 - 5x + 6 = 0, what are the roots?

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