Limit your limits!

Calculus Level 5

A = lim ⁡ x → 0 ( 1 + arctan ( arcsin ( x ) ) + arctan ( arcsin ( 2 x ) ) + ⋯ + arctan ( arcsin ( n x ) ) ) 1 arcsin ( n x ) A=\lim_{x\rightarrow 0} (1+\text{arctan}(\text{arcsin}(x))+\text{arctan}(\text{arcsin}(2x))+\cdots+\text{arctan}(\text{arcsin}(nx)))^{\frac{1}{\text{arcsin}(nx)}}

What is the value of ⌊ A ⌋ \lfloor A \rfloor when n = 10 n=10 ?


The answer is 244.

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Jafar Badour by jafar badour , 23, Russia

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1 solution

Ajay Saju
Jan 29, 2016

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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