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

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Remainder Hunt

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

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Prove that the sum from t=0 to m of (-1)^t/t!(m-t)! is zero.


Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Consider powers of $1 + x$.

If you can't get started investigate the formula for $n = 2, 3,4 ...$