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### Telescoping Series

##### Stage: 5 Challenge Level:

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

### The Harmonic Triangle and Pascal's Triangle

##### Stage: 5

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

### The Kth Sum of N Numbers

##### Stage: 5

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