\(\dfrac{1}{1\times2}\) + \(\dfrac{1}{2\times3}\) + \(\dfrac{1}{3\times4}\) + ......+ \(\dfrac{1}{99\times100}\)

 = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + .....+ \(\dfrac{1}{99}\) - \(\dfrac{1}{100}\)

= 1 - \(\dfrac{1}{100}\)

= \(\dfrac{99}{100}\)

A = \(\dfrac{7}{15}\) : \(\dfrac{19}{5}\) + \(\dfrac{8}{15}\) : \(\dfrac{19}{5}\)

A = ( \(\dfrac{7}{15}\) + \(\dfrac{8}{15}\) ) : \(\dfrac{19}{5}\)

A = 1 : \(\dfrac{19}{5}\)

A = 5/19

\(\dfrac{35}{14}\)+ \(\dfrac{21}{7}\)- \(\dfrac{3}{4}\) = \(\dfrac{70}{28}\) + \(\dfrac{84}{28}\) - \(\dfrac{21}{28}\) = \(\dfrac{133}{28}\)= \(\dfrac{19}{4}\)

 

\(\dfrac{35}{14}\) + \(\dfrac{21}{7}\)- \(\dfrac{3}{4}\)= \(\dfrac{70}{28}\)+ \(\dfrac{84}{28}\) - \(\dfrac{21}{28}\) = \(\dfrac{133}{28}\) = \(\dfrac{19}{4}\)

\(\dfrac{1}{2}\) x + \(\dfrac{2}{3}\) x - 1 =-3\(\dfrac{1}{3}\)

x ( \(\dfrac{1}{2}\)+ \(\dfrac{2}{3}\)) -1 = - \(\dfrac{10}{3}\)

x \(\dfrac{7}{6}\) - 1 = - \(\dfrac{10}{3}\)

\(\dfrac{7}{6}\)x  = -  \(\dfrac{10}{3}\)+ 1

\(\dfrac{7}{6}\)x = - \(\dfrac{7}{3}\)

x =- \(\dfrac{7}{3}\) : \(\dfrac{7}{6}\)

x = -2

 

\(\dfrac{1}{2}\) x + \(\dfrac{2}{3}\) x - 1 = -3\(\dfrac{1}{3}\) 

\(\dfrac{1}{2}\) x + \(\dfrac{2}{3}\) x - 1 = - \(\dfrac{10}{3}\) x (\(\dfrac{1}{2}\) + \(\dfrac{2}{3}\))  = - \(\dfrac{10}{3}\) + 1  x . \(\dfrac{7}{6}\) = -\(\dfrac{7}{3}\) x = -\(\dfrac{7}{3}\) : \(\dfrac{7}{6}\) x = -2   

-(x-2)² ≤ 0

-3  - (x-2)² ≤ -3

D(max )= -3 dấu = xảy ra khi x = 2