Question

ayúdenme por favor :(​

Answer 1

Respuesta:

x = 98

Explicación paso a paso:

Resolver:

$\frac{99}{2} + \frac{99}{6} + \frac{99}{12} + ... + \frac{99}{ {x}^{2} + x} = 98$

$99( \frac{1}{2} + \frac{1}{6} + \frac{1}{12} + ... + \frac{1}{ {x}^{2} + x} ) = 98$

$\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + ... + \frac{1}{ {x}^{2} + x } = \frac{98}{99}$

$\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + ... + \frac{1}{x \cdot (x + 1)} = \frac{98}{99}$

$\frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{x} - \frac{1}{x + 1} = \frac{98}{99}$

$\frac{1}{1} - \cancel{ \frac{1}{2} + \frac{1}{2} } - \cancel{\frac{1}{3} + \frac{1}{3} } - \cancel{ \frac{1}{4} + }... \cancel{+ \frac{1}{x} } - \frac{1}{x + 1} = \frac{98}{99}$

$\frac{1}{1} - \frac{1}{x + 1} = \frac{98}{99}$

$\frac{x + 1}{x + 1} - \frac{1}{x + 1} = \frac{98}{99}$

$\frac{x + 1 - 1}{x + 1} = \frac{98}{99}$

$\frac{x}{x + 1} = \frac{98}{99}$

$99x = 98(x + 1)$

$99x = 98x + 98$

$99x - 98x = 98$

$x = 98$