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 Jun3 awarded Popular Question Apr18 awarded Nice Question Mar10 revised Proving $(2n+1) + (2n+3) + \cdots + (4n-1) = 3n^{2}$ for all positive integers $n$ removed ">" from formatted text block Mar9 awarded Nice Question Mar3 awarded Popular Question Mar1 awarded Popular Question Jan8 awarded Popular Question Nov19 awarded Yearling Nov1 awarded Popular Question Oct26 awarded Popular Question Jun8 awarded Constituent Jun8 awarded Caucus Nov19 awarded Yearling Sep23 accepted Why exactly can you take the absolute value of one side of this inequality and assume it is still true? Sep22 asked Why exactly can you take the absolute value of one side of this inequality and assume it is still true? Sep20 accepted Why is it that $\left|b_n - b \right| < \frac{\left|b \right|}{2} \Rightarrow \left| b_n \right| > \frac{\left|b \right|}{2}$? Sep20 comment Why is it that $\left|b_n - b \right| < \frac{\left|b \right|}{2} \Rightarrow \left| b_n \right| > \frac{\left|b \right|}{2}$? Thanks to all of you for your help! Part of what I overlooked is that $|b_n - b| = |b - b_n|$... I think I was trying to do this, but I kept getting $\frac{3|b|}{2}$ or something... Anyway, I think it makes sense to me finally :) Sep20 asked Why is it that $\left|b_n - b \right| < \frac{\left|b \right|}{2} \Rightarrow \left| b_n \right| > \frac{\left|b \right|}{2}$? Sep7 accepted What is the explanation for the elements of this set? Sep7 revised What is the explanation for the elements of this set? edited body