(x/(1×2)) + (x/(2×3)) + (x/(3×4)) + ......+ (x/(1998×1999)) + (x/(1999×2000)) = 1 x = ????


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Question Number 189761 by normans last updated on 21/Mar/23

$\frac{x}{1 \times 2} + \frac{x}{2 \times 3} + \frac{x}{3 \times 4} + . . . . . . + \frac{x}{1998 \times 1999} + \frac{x}{1999 \times 2000} = 1$ $x = ? ? ? ?$
	Answered by Frix last updated on 21/Mar/23

	$\underset{k = 1}{\sum^{n}} \frac{x}{k (k + 1)} = \frac{x n}{n + 1} = 1 \Rightarrow x = \frac{n + 1}{n}$
	Answered by BaliramKumar last updated on 21/Mar/23

	$x [\frac{1}{1} - \frac{1}{2000}] = 1$ $x [\frac{2000 - 1}{2000}] = 1$ $x = \frac{2000}{1999}$
	Answered by manxsol last updated on 21/Mar/23

	$x (1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + . . . . . \frac{1}{1999} - \frac{1}{2000}) = 1$ $x (1 - \frac{1}{2000}) = 1$ $x = \frac{2000}{1999}$
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