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Growing

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

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Binomial

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

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Remainder Hunt

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

Summit

Stage: 5 Challenge Level: Challenge Level:1

Prove that the sum

$$ \sum_{t=0}^m {(-1)^t\over t!(m-t)!} = 0 $$