Factorials

article
Binomial Coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
problem

N000ughty Thoughts

Age

14 to 16

Challenge level

How many noughts are at the end of these giant numbers?
problem

Seriesly

Age

16 to 18

Challenge level

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!
problem

How Does Your Function Grow?

Age

16 to 18

Challenge level

Compares the size of functions f(n) for large values of n.
problem

Growing

Age

16 to 18

Challenge level

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)
problem
Favourite

Fac-Finding

Age

14 to 16

Challenge level

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.
problem

Squaresearch

Age

14 to 16

Challenge level

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?
problem

Trailing Zeros

Age

11 to 14

Challenge level

How many zeros does 50! have at the end?
problem

Factorised Factorial

Age

14 to 16

Challenge level

Weekly Problem 17 - 2010
The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?
problem

Forgotten Number

Age

11 to 14

Challenge level

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...