$B=$$\frac{1}{9×10}$$-$$\frac{1}{8×9}$ $-....-$ $\frac{1}{1×2}$
$B=-$$($$\frac{1}{8×9}$ $+....+$ $\frac{1}{1×2}$$-$$\frac{1}{9×10}$$)$
$B=-$($\frac{1}{1×2}$ $+....+$ $\frac{1}{8×9}$$-$$\frac{1}{9×10}$$)$
$B=-$($\frac{1}{1×2}$ $+....+$ $\frac{1}{8×9}$$-$$\frac{1}{9×10}$$)$
$B=-$$($$\frac{1}{1}$$-$$\frac{1}{2}$$+...+$$\frac{1}{8}$$-$$\frac{1}{9}$$-$$\frac{1}{90}$$)$
$B=-$$($$\frac{1}{1}$$-$$\frac{1}{9}$$-$$\frac{1}{90}$$)$
$B=-$$\frac{79}{90}$
