Summation of series

problem
Overarch 2

Age

16 to 18

Challenge level

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?
problem
OK! Now prove it

Age

16 to 18

Challenge level

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?
problem
Degree ceremony

Age

16 to 18

Challenge level

Can you find the sum of the squared sine values?
problem
Telescoping series

Age

16 to 18

Challenge level

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

A story for students about adding powers of integers - with a festive twist.
article
An introduction to mathematical induction

This article gives an introduction to mathematical induction, a powerful method of mathematical proof.
article
The kth sum of n numbers

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

Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.
article
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.
interactivity
Proof sorter - geometric sequence

Age

16 to 18

Challenge level

Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?