Factorials

article
The harmonic triangle and Pascal's triangle

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.
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
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...
problem
Factorial

Age

14 to 16

Challenge level

How many zeros are there at the end of the number which is the product of first hundred positive integers?
problem
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?