Summation of series

problem
Summing squares

Age

14 to 16

Challenge level

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
problem
Summing geometric progressions

Age

14 to 18

Challenge level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
problem
The root of the problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.
problem
Vanishing point

Age

14 to 18

Challenge level

How can visual patterns be used to prove sums of series?
problem
Degree ceremony

Age

16 to 18

Challenge level

Can you find the sum of the squared sine values?
problem
Clickety click and all the sixes

Age

16 to 18

Challenge level

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
problem
Succession in Randomia

Age

16 to 18

Challenge level

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?
problem
Seriesly

Age

16 to 18

Challenge level

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!
problem
Speedy summations

Age

16 to 18

Challenge level

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
problem
A swiss sum

Age

16 to 18

Challenge level

Can you use the given image to say something about the sum of an infinite series?