Resources tagged with: Binomial Theorem

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There are 12 results

Broad Topics > Algebraic expressions, equations and formulae > Binomial Theorem

Tens

Age 16 to 18 Challenge Level:

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

Telescoping Series

Age 16 to 18 Challenge Level:

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

Growing

Age 16 to 18 Challenge Level:

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

Elevens

Age 16 to 18 Challenge Level:

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

Bina-ring

Age 16 to 18 Challenge Level:

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

Remainder Hunt

Age 16 to 18 Challenge Level:

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

Summit

Age 16 to 18 Challenge Level:

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

The Kth Sum of N Numbers

Age 16 to 18

Yatir from Israel describes his method for summing a series of triangle numbers.

The Harmonic Triangle and Pascal's Triangle

Age 16 to 18

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.

Binomial Coefficients

Age 14 to 18

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

Binomial

Age 16 to 18 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

Discrete Trends

Age 16 to 18 Challenge Level:

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