prove the existence of n integrs naturals x_1 ,x_2 ,....x_n with x_i ≠x_j for i≠j and (1/x_1 ) +(1/x_2 ) +....+(1/x


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Question Number 49095 by maxmathsup by imad last updated on 02/Dec/18

$p r o v e t h e e x i s t e n c e o f n i n t e g r s n a t u r a l s x_{1}, x_{2}, . . . . x_{n} w i t h x_{i} \neq x_{j} f o r i \neq j$ $a n d \frac{1}{x_{1}} + \frac{1}{x_{2}} + . . . . + \frac{1}{x_{n}} = 1 .$
	Answered by kwonjun1202 last updated on 03/Dec/18
	$1=0.5+0.25+0.125+0.0625+0.003125... =(5/(10)) +(5^2 /(10^2 )) +(5^3 /(10^3 )) +....+((5/(10)))^n reduce a fraction =(1/2^n ) ∴Σ_(n=1) ^∞ (1/2^n ) =1,$
	$1 = 0.5 + 0.25 + 0.125 + 0.0625 + 0.003125 . . .$ $= \frac{5}{10} + \frac{5^{2}}{10^{2}} + \frac{5^{3}}{10^{3}} + . . . . + {(\frac{5}{10})}^{n} r e d u c e a f r a c t i o n = \frac{1}{2^{n}}$ $∴ \underset{n = 1}{\sum^{\infty}} \frac{1}{2^{n}} = 1,$
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