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NRICH topics: Algebraic expressions, equations and formulae Binomial theorem

Resources tagged with: Binomial theorem

Content type:
Age range:
Challenge level:

There are 12 NRICH Mathematical resources connected to Binomial theorem, you may find related items under Algebraic expressions, equations and formulae.

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

Problem Primary curriculum Secondary curriculum

Tens

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

Age 16 to 18
Challenge Level Yellow starYellow star
Problem Primary curriculum Secondary curriculum

Discrete Trends

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

Age 16 to 18
Challenge Level Yellow starYellow star
Problem Primary curriculum Secondary curriculum

Summit

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

Age 16 to 18
Challenge Level Yellow star
Problem Primary curriculum Secondary curriculum

Binomial

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

Age 16 to 18
Challenge Level Yellow starYellow star
Problem Primary curriculum Secondary curriculum

Telescoping Series

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

Age 16 to 18
Challenge Level Yellow starYellow star
Article Primary curriculum Secondary curriculum

Binomial Coefficients

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

Age 14 to 18
Problem Primary curriculum Secondary curriculum

Bina-ring

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

Age 16 to 18
Challenge Level Yellow starYellow starYellow star
Problem Primary curriculum Secondary curriculum

Elevens

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

Age 16 to 18
Challenge Level Yellow star
Article Primary curriculum Secondary curriculum

The Harmonic Triangle and Pascal's Triangle

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

Age 16 to 18
Article Primary curriculum Secondary curriculum

The Kth Sum of N Numbers

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

Age 16 to 18
Problem Primary curriculum Secondary curriculum

Remainder Hunt

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

Age 16 to 18
Challenge Level Yellow starYellow star
Problem Primary curriculum Secondary curriculum

Growing

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

Age 16 to 18
Challenge Level Yellow starYellow star

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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