Summation notation can strike fear into the hearts of the un-prepared.

Once you get the hang of it, it is actually quite a conveniant notation.

Summation notation is a shorthand that mathematicians use when there is a lot (sometimes an infinite lot) of adding up to be done in an equation or expression.

Here are a few examples:

Here “i” goes from 1 to 5 (inclusive) and for each occurrence we simply add whatever value i is currently onto what we have so far.

Lets up the pace a little

Ooooh, a 3 raised to the power of something, but what?

Iit is quite simple really...

Let's get a little bit recursive…

Oh my gawd!! What does that mean?

And we can get even more complicated!!!

A little bit more recursive and a lot bigger!!!!

Quite easy really.

Further examples where the indices are used as a labels. For instance in statistics. Where it might symbolise the ith (or jth) value obtained in a statistical experiment. In this case the i (or j) would not be an actual number in the function (like above) but would represent a specific value from the sample set.

Summation notation has been truncated further still in Einstein notation which is used in Tensor Calculus.

I'll write up some examples of Einstein Notation once I have given it a good reading in the book I've got.

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