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Telescoping Series
Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.
Degree Ceremony
What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?
OK! Now Prove It
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?
Age 14 to 18
Challenge Level
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Think about other ways to write $\frac{1}{\sqrt{n}+\sqrt{n+1}}$, particularly ways that have no surds in the denominator.
Think about other ways to write $\frac{1}{\sqrt{n}+\sqrt{n+1}}$, particularly ways that have no surds in the denominator.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.