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A=tan−1(12)+tan−1(13)+tan−1(14)B=π2\begin{aligned} A &=& \tan^{-1} \left( \frac 1 {\sqrt2} \right)+ \tan^{-1} \left( \frac 1 {\sqrt3} \right) + \tan^{-1} \left( \frac 1 {\sqrt4} \right) \\ \\ B & = & \frac {\pi}{2} \\ \end{aligned} AB==tan−1(21)+tan−1(31)+tan−1(41)2π
Without resorting to tables or calculator, determine which of these numbers above is larger.
All credit for this problem goes to Pi Han Goh.
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