Crazy Comparing

Algebra Level 4

Let A=[(x+1)(x+2)2]2[x(x+1)2]2A=\bigg[\frac{(x+1)(x+2)}{2}\bigg]^2-\bigg[\frac{x(x+1)}{2}\bigg]^2 B=(x1)(3x21)+i=1x2i2(x2)(x12)2+x(x+2)B=(x-1)(\frac{3x}{2}-1)+\frac{\displaystyle \sum_{i=1}^{x-2} i^2-(x-2)(\frac{x-1}{2})}{2}+x(x+2) Here, xx is a positive integer. Which is bigger, AA or 2B2B?


This is one part of 1+1 is not = to 3.
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