Summation of series

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

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

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

Simple additions can lead to intriguing results...

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

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

Find the smallest value for which a particular sequence is greater than a googol.

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

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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