Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Sum the Series
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Sum the series

This article by Alex Goodwin, age 18 of Madras College, St Andrews describes how to find the sum of 1 + 22 + 333 + 4444 + ... to n terms.
Why stop at Three by One
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Why stop at three by one

Beautiful mathematics. Two 18 year old students gave eight different proofs of one result then generalised it from the 3 by 1 case to the n by 1 case and proved the general result.
Magic Squares
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Magic squares

An account of some magic squares and their properties and and how to construct them for yourself.
Magic Squares II
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Magic squares ii

An article which gives an account of some properties of magic squares.
Fractional Calculus I
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Fractional calculus i

You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.
Fractional Calculus II
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Fractional calculus ii

Here explore some ideas of how the definitions and methods of calculus change if you integrate or differentiate n times when n is not a whole number.
Fractional Calculus III
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Fractional calculus iii

Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.
Go Forth and Generalise
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Go forth and generalise

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.