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 18
Challenge Level

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

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!

Seriesly

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!

Squaresearch

Age 14 to 16
Challenge Level

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

N000ughty Thoughts

Age 14 to 16
Challenge Level

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

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.

Factorial Fun

Age 16 to 18
Challenge Level

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

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?

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)

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.