# Crazy Comparing

Algebra Level 4

Let $A=\bigg[\frac{(x+1)(x+2)}{2}\bigg]^2-\bigg[\frac{x(x+1)}{2}\bigg]^2$ $B=(x-1)(\frac{3x}{2}-1)+\frac{\displaystyle \sum_{i=1}^{x-2} i^2-(x-2)(\frac{x-1}{2})}{2}+x(x+2)$ Here, $x$ is a positive integer. Which is bigger, $A$ or $2B$?

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