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

The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

View Question

A sphere has a radius of 7 cm. What is its volume?

View Question

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

View Question

What is the remainder when 5^100 is divided by 3?

View Question

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

View Question

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

View Question

If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

View Question

The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

View Question

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

View Question

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

View Question