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 number is increased by 20% and then decreased by 10%. What is the net change?

View Question

The sum of the squares of two consecutive integers is 145. What are the integers?

View Question

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

View Question

A man spends 75% of his income and saves Rs. 600. What is his total income?

View Question

The sides of a triangle are 7, 24, and 25. Is this a right triangle?

View Question

If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

View Question

How many diagonals does a pentagon have?

View Question

If 2x - 3 = 7, what is the value of x?

View Question

A cube has a side length of 4 cm. What is its volume?

View Question

If a person can type 45 words per minute, how many words can they type in 2 hours?

View Question