article

### Binomial Coefficients

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

article
###
Binomial Coefficients

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

problem
###
Tens

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

problem
###
Discrete Trends

Find the maximum value of n to the power 1/n and prove that it is a
maximum.

problem
###
Remainder Hunt

What are the possible remainders when the 100-th power of an
integer is divided by 125?

problem
###
Binomial

By considering powers of (1+x), show that the sum of the squares of
the binomial coefficients from 0 to n is 2nCn

problem
###
Growing

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

problem
###
Telescoping series

Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.