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Resources tagged with Binomial Theorem similar to The Harmonic Triangle and Pascal's Triangle:

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Summit

Stage: 5 Challenge Level:

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

Growing

Stage: 5 Challenge Level:

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

Discrete Trends

Stage: 5 Challenge Level:

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

Tens

Stage: 5 Challenge Level:

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

Elevens

Stage: 5 Challenge Level:

Add powers of 3 and powers of 7 and get multiples of 11.

Binomial

Stage: 5 Challenge Level:

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

Remainder Hunt

Stage: 5 Challenge Level:

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

Bina-ring

Stage: 5 Challenge Level:

Investigate powers of numbers of the form (1 + sqrt 2).