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.

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 is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.

Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.

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In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?

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