According to my friend, who is in the International Maths
Olympiad squad of Singapore, the problem lies with these 2
lines.
The first of these 2 is correct. However, the problem is when you
try to square root both sides. On the surface, the operation looks
valid. However, on the right, the expression can be rewritten
as:
n - 1/2(2n+1) = n - 1/2*2n - 1/2 = n - n -1/2 = -1/2.
Since the square root of any negative number of undefined, the
proof is thus rendered invalid.
The fallacy is not easy to spot.
For more such stuffs, if you have spare time and feel boliao, visit
here.
http://en.wikipedia.org/wiki/Invalid_proof
