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Geometric Series

Let's try it:

the summation of 3 * ( 1 / 2 )^( k - 1 ) = 3 / ( 1 - ( 1 / 2 ) ) = 3 / (1 / 2 ) = 6 ... a1 is 3 ... r is ( 1 / 2 )

No! Duuuuuude!

How can this be?!

You mean to tell me that

3 + ( 3 / 2 ) + ( 3 / 4 ) + ( 3 / 8 ) + ( 3 / 16 ) + ( 3 / 32 ) + ... = 6 ?!
 

But, that's an infinite number of numbers!  This is madness!  My head hurts.

OK, settle down...  Let me convince you that this is possible.

Look at this:

( 1 / 2 ) + ( 1 / 4 ) + ( 1 / 8 ) + ( 1 / 16 ) + ...

Let's add it on a big number line:

number line from 0 to 1

Let's add one term at a time...

number line from 0 to 1 ... add ( 1 / 2 )