please solve : lim_(n→∞) ((1 +(√2) +(3)^(1/3) +(4)^(1/4) +......((2n))^(1/(2n)) )/(3n−4)) =???


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Question Number 109736 by mnjuly1970 last updated on 25/Aug/20

$p l e a s e s o l v e :$ ${l i m}_{n \to \infty} \frac{1 + \sqrt{2} + \sqrt[3]{3} + \sqrt[4]{4} + . . . . . . \sqrt[2 n]{2 n}}{3 n - 4}$ $= ? ? ?$
	Answered by Her_Majesty last updated on 25/Aug/20

	$f o r v e r y h i g h v a l u e s o f n a l m o s t a l l t e r m s$ $\sqrt[n]{n} a r e e q u a l t o 1 \Rightarrow w e h a v e \sim \frac{2 n}{3 n - 4} w h i c h$ $i s e q u a l t o \frac{2}{3} w h e n n \to \infty$
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