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Series and Sigma Notation

Here are some basic guys that you'll need to know the sigma notation for:

THE EVENS:

the summation of 2k as k goes from 1 to infinity will generate 2 + 4 + 6 + 8 + ...
the summation of 2k as k goes from 1 to infinity ... notice the infinity

This means the series goes on forever and ever.

If you want to generate

0 + 2 + 4 + 6 + 8 + ...

what would you need to change?

the summation of 2k as k goes from 0 to infinity ... start the index at 0!

THE ODDS:

Odd numbers are just evens plus one...

the summation of ( 2k + 1 ) as k goes from 0 to infinity = 1 + 3 + 5 + 7 + ...

Or you can think of odd numbers as evens minus one...

the summation of ( 2k - 1 ) as k goes from 1 to infinity = 1 + 3 + 5 + 7 + ...

Wait a minute!  What just happened here?!

the summation of ( 2k + 1 ) as k goes from 0 to infinity and the summation of ( 2k - 1 ) as k goes from 1 to infinity
Here's what happened...               
These guys started at different places.

So, be careful and ALWAYS check the first few terms to make sure that everything works!

Does this guy generate ALL the odds?

the summation of ( 2k + 1 ) as k goes from 1 to infinity