article
The kth sum of n numbers
Yatir from Israel describes his method for summing a series of
triangle numbers.
Binomial theorem
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articleThe harmonic triangle and Pascal's triangle
The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.
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articleBinomial coefficients
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
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problemSummit
Age16 to 18Challenge level
Prove that the sum from t=0 to m of (-1)^t/t!(m-t)! is zero. -
problemElevens
Age16 to 18Challenge level
Add powers of 3 and powers of 7 and get multiples of 11. -
problemGrowing
Age16 to 18Challenge level
Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300) -
problemBinomial
Age16 to 18Challenge level
By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn -
problemRemainder hunt
Age16 to 18Challenge level
What are the possible remainders when the 100-th power of an integer is divided by 125? -
problemDiscrete trends
Age16 to 18Challenge level
Find the maximum value of n to the power 1/n and prove that it is a maximum. -
problemBina-ring
Age16 to 18Challenge level
Investigate powers of numbers of the form (1 + sqrt 2).