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Sequences and Series
Challenge level
Sequences are everywhere in mathematics! In these problems you can explore some sequences, learn how to represent them, and how to calculate sums of series.
problem
Summats clear
Age
16 to 18
Challenge level
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1,
2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a
- b) = ab.
problem
Be reasonable
Age
16 to 18
Challenge level
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
progression.
problem
Favourite
Harmonically
Age
16 to 18
Challenge level
Is it true that a large integer m can be taken such that: 1 + 1/2 +
1/3 + ... +1/m > 100 ?
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Prepare for university - pure mathematics
Helpful preparation for those intending to study a course involving pure mathematics at university.
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Prepare for university - applied mathematics
Helpful preparation for university for those intending to study a
course involving applied mathematics at university.
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NRICH and Olympiads
A useful entry point into the NRICH site for those students interested in Mathematical Olympiad problems or the Maths Challenges.