Right, first contemplate what is a string or a sequence of numbers:

1, 1/2, 1/3, 1/4, 1/5

if we dot it at the end like so,

1, 1/2, 1/3, 1/4, 1/5...

It means, ''and so on,'' in this particular pattern. We can now say that the n^th number is a_n, then one can evaluate that a_1 is 1, and a_2 is 1/2, so that implies that a_n=1/n. An infinite series of numbers will look something like this:

∑ = 1 + 1/2 + 1/4 + 1/8 + ...

Where again, the (+ ...) means an infinite continuation of the numerical processes. Since we can't add all of infinite numbers, we can however add the first lot of ''n'' terms like

∑_1 = 1

∑_2 = 1 + 1/2 = 3/2

∑_3 = 1 + 1/2 + 1/4 = 7/4

where ∑ just means the 'sum of.'

Does that help?