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Binomial Coefficients
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
Factorials
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
Factorised Factorial
Age
14 to 16
Challenge level
Weekly Problem 17 - 2010
The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?
The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?
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
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
Powerful factorial
Age
11 to 14
Challenge level
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides
exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest
power of two that divides exactly into 100!?
problem
Factoring factorials
Age
11 to 14
Challenge level
Find the highest power of 11 that will divide into 1000! exactly.
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?