SOLUTION: 1^2+3^2+5^2+.....+n^2. What kind of series it is?

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Question 1043036: 1^2+3^2+5^2+.....+n^2. What kind of series it is?



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is the sum of squares of the first n odd natural numbers..

Also, the last term is written incorrectly. It should be %282n-1%29%5E2.

If you want to know the sum and how to get it, then see the lesson
    - Mathematical induction for sequences other than arithmetic or geometric
in this site.

The sum 1%5E2%2B2%5E2%2B3%5E2%2B+ellipsis+%2Bn%5E2 was calculated there of squares of the first n natural numbers.

To get what you want (? if you want it ?), take this sum from 1 to (2n-1) and then distract the sum of squares of all even numbers from 2 to (2n).