Grandi’s Series

If you look at the series:

S = 1 – 1 + 1 -1 + 1 -1 …to infinity
the sum turns out to be , S=0.

Now , if we look it in another way

S = 1 -(1-1) – (1-1) – (1-1)…to infinity
the Sum turns out to be , S=1

The result is either 0 or 1.

The most interesting part comes now.
A priest and Mathematician named Grandi, presented an alternate but mind boggling proof for the summation.

Let us say ,
S = 1-1+1-1+1-1…

Now say,
S = 1-(1-1+1-1+1 …)

So that makes it,
2S = 1
S =1/2

The most fun part is the result , sum of all the integers being a fraction (1/2).

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Document Object Model

Document Object Model  is an API or a web framework for programmers to access, update ,delete, or do anything with an HTML or XML document.

It works in JavaScript and J Query , and consists of a definite structure for the elements present inside an HTML,XML,J SON Document.

It defines the correct format and order  for a  valid HTML or a well formed XML.

It is maintained and standardized by   World Wide Web consortium. DOM is platform and language independent model which works with documents generated by any platform or server side script.