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Question Number 107080 by Khalmohmmad last updated on 08/Aug/20

	Answered by abdomsup last updated on 08/Aug/20
	$A_n =((n^n {(n/n^n )+(n^2 /n^n )+....+1})/(n^n {(1/n^n ) +((2/n))^(n ) +((3/n^ ))^n +....1})) A_n =(((1/n^(n−1) )+(1/n^(n−2) )+....+1)/(((1/n))^n +((2/n))^n +...+1)) ⇒ lim_(n→+∞) A_n =1$
	$A_{n} = \frac{n^{n} {\frac{n}{n^{n}} + \frac{n^{2}}{n^{n}} + . . . . + 1}}{n^{n} {\frac{1}{n^{n}} + {(\frac{2}{n})}^{n} + {(\frac{3}{n^{}})}^{n} + . . . . 1}}$ $A_{n} = \frac{\frac{1}{n^{n - 1}} + \frac{1}{n^{n - 2}} + . . . . + 1}{{(\frac{1}{n})}^{n} + {(\frac{2}{n})}^{n} + . . . + 1} \Rightarrow$ ${l i m}_{n \to + \infty} A_{n} = 1$
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