Find the largest positive integer such that is a perfect square.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
The only two values of n for which the indicated series has a Sum which is a perfect square are: 1 and 24.
If n = 1 the Sum is 1 and if n = 2 4 the Sum is 4 9 0 0 I have checked for 1 ≤ n ≤ 1 , 0 0 0 , 0 0 0 while killing time in the hospital using just my TI 84+ calculator.
So, the largest value of n is 2 4
Also, you can check out A000330 on OEIS for further information.
A more general situation with proofs is discussed here .