I was hoping someone would be able to tell me the name of this technique (described below) I used so I can go away and do some reading about it and hopefully learn it in a more structured way. Also if there are any similar techniques for deducing polynomials from series (like expanding the series) could you tell me the names of them so I can do some reading about them too. Or any other techniques for finding the sum of squares. Thanks.
So I was trying to deduce the sum of squares:
and I used the technique where you go down the levels of the difference. i.e
the first few terms of this series is:
difference of these terms is:
and the diff. of the diff.:
and the level 3 diff.:
so now we can see that since it's level 3 .
comparing this to series:
comparing level 3's of and we get:
Now the level 2 difference of is:
and level 2 difference for is:
so we now have:
Finally the level 1 difference of is:
and for is:
and I got the right result. Now what's this technique called?