x-1-2-x-2-3-x-3-4-x-1998-1999-x-1999-2000-1-x-

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} + \dots \dots + \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} + \dots . . \frac{1}{1999} - \frac{1}{2000}) = 1

x (1 - \frac{1}{2000}) = 1

x = \frac{2000}{1999}

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