Wolframに具体的に計算してもらった方が分りやすいな。

https://www.wolframalpha.com/input/
?i=lim(x→(1%2F(√3)))6x%2F(1%2B((1x)^2)%2F(3%2B((2x)^2)%2F(5%2B((3x)^2)%2F(7%2B((4x)^2)%2F(9%2B((5x)^2)%2F(11%2B((6x)^2)%2F(13%2B((7x)^2)%2F(15%2B((8x)^2)%2F(17%2B((9x)^2)%2F19)))))))))