At first I write it about 1
What do you associate about 1?Number 1 is used everywhere. So to associative is easy.For example you might think of pitcher if you like baseball.You might think of goalkeeper if you like football.You might think of hydrogen if you like chemistry.
It's good knowledge fairly not matter, but the world weight of sand of large hourglass is 1kg.
Now, let us look one from a mathematical point of view.
There are following something like the famous infinite series of about 1
The question is,What is the value of, (1/2) + (1/4) + (1/8) ...... ?The reason an infinite sum like 1 + 1/2 + 1/4 + · · · can have a definite value is that one is really looking at the sequence of numbers
1/2 = 1/2
1/2 + 1/4 = 3/4
1/2 + 1/4 + 1/8 = 7/8
etc.,
and this sequence of numbers (1/2, 3/4, 7/8, . . . ) is converging to a limit.
It is this limit which we call the "value" of the infinite sum.
How do we find this value?
If we assume it exists and just want to find what it is, let's call it S. Now
S = 1/2 + 1/4 + 1/8 + · · ·
so, if we multiply it by 1/2, we get
(1/2) S = 1/4 + 1/8 + 1/16 + · · ·
Now, if we subtract the second equation from the first, the 1/4, 1/8, etc. all cancel, and we get S - (1/2)S = 1/2 which means S/2 = 1/2 and so S = 1.
