# Resources tagged with: Factorials

### There are 11 results

Broad Topics >

Properties of Numbers > Factorials

##### Age 16 to 18

Challenge Level

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

##### 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 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!

##### 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

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

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

##### 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

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 14 to 18

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