Can anyone explain the working out for this? Is there a method that you are supposed to use?

Question: Write this series in sigma notation.

1+1/2+1/4+...+1/512

Also in some examples I have seen like 3+6+12+...+3×2(power n) you are supposed to change the 'n' to a 'k'. Why is that?

Hi there,

Noticing that the terms in your series are all 1 divided by increasing powers of 2 (i.e. 2^0, 2^1, 2^2, up to 2^9), we'd write something like this:

The bottom is where n begins (0 in this case for our first term of 1) and the top number is when we finish. You can use trial and error without too much fuss to see what power of 2 that 512 is raised to. Alternatively, you could use logarithms, which is a later topic in the maths course. Here, log

_{2}512 = 9. We use n as our only variable as this is a finite series, which will stop when we finish adding 1/512 to our sum.

On the right, is what we're summing over and over again, with different values of n for each time we do it. Hopefully I'm making some sense.

We generally use k if the sum's final term is in general form (i.e. all the terms in this series follow this rule, where k is replaced by the term number). It will either denote some value that we either need to find, or don't need to worry about. It's essentially the math's conventional placeholder, which isn't a major focus of the course anyway, but to see an example of it in action:

So yeah, it's more focusing on the process of summation rather than the answer. Let me know if I'm not making sense