# Resources tagged with: Factorials

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### There are 11 results

Broad Topics > Properties of Numbers > Factorials

### How Does Your Function Grow?

##### Age 16 to 18Challenge Level

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

### Seriesly

##### Age 16 to 18Challenge Level

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

### Seriesly

##### Age 16 to 18 ShortChallenge Level

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

### Squaresearch

##### Age 14 to 16Challenge Level

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

### N000ughty Thoughts

##### Age 14 to 16Challenge Level

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

### Fac-finding

##### Age 14 to 16Challenge 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.

### Factorial Fun

##### Age 16 to 18Challenge Level

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

### Factorial

##### Age 14 to 16Challenge Level

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

### Growing

##### Age 16 to 18Challenge Level

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

### The Harmonic Triangle and Pascal's Triangle

##### Age 16 to 18

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

### Binomial Coefficients

##### Age 14 to 18

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