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Resources tagged with Binomial Theorem similar to Golden Powers:

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Broad Topics > Advanced Algebra > Binomial Theorem

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Bina-ring

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Elevens

Stage: 5 Challenge Level: Challenge Level:1

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

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Tens

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

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

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Growing

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

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

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Summit

Stage: 5 Challenge Level: Challenge Level:1

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

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Discrete Trends

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

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

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Remainder Hunt

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

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

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Binomial

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

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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