# Resources tagged with: Factorials

### There are 11 results

Broad Topics >

Numbers and the Number System > Factorials

##### Age 16 to 18 Challenge Level:

How many divisors does factorial n (n!) have?

##### Age 14 to 18

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

##### Age 14 to 16 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

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

##### 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?

##### 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!

##### 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.

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18

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

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Short Challenge Level:

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