\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{13\cdot14}+\frac{1}{14\cdot15}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{14}-\frac{1}{15}\)

\(=\frac{1}{2}-\frac{1}{15}\)

\(=\frac{13}{30}\)

Lời giải:

$3S=10.11(12-9)+11.12(13-10)+12.13(14-11)+...+98.99(100-97)+99.100(101-98)$

$=(10.11.12+11.12.13+12.13.14+...+98.99.100+99.100.101)-(9.10.11+10.11.12+...+97.98.99+98.99.100)$

$=99.100.101-9.10.11$

$\Rightarrow S=\frac{99.100.101-9.10.11}{3}=33.100.101-3.10.11$

\(\dfrac{3}{10.11}\) + \(\dfrac{3}{11.12}\) + \(\dfrac{3}{12.13}\) + \(\dfrac{3}{13.14}\) + \(\dfrac{3}{14.15}\)

= \(\dfrac{3}{10}\) - \(\dfrac{3}{11}\) + \(\dfrac{3}{11}\) - \(\dfrac{3}{12}\) + \(\dfrac{3}{12}\) - \(\dfrac{3}{13}\) + \(\dfrac{3}{13}\) - \(\dfrac{3}{14}\) + \(\dfrac{3}{14}\) - \(\dfrac{3}{15}\)

= \(\dfrac{3}{10}\) - \(\dfrac{3}{15}\) = \(\dfrac{1}{10}\)

\(\dfrac{3}{10.11}+\dfrac{3}{11.12}+\dfrac{3}{12.13}+\dfrac{3}{13.14}+\dfrac{3}{14.15}\)

\(=\dfrac{3}{1}.\left(\dfrac{3}{10}-\dfrac{3}{11}+\dfrac{3}{11}-\dfrac{3}{12}+\dfrac{3}{12}-\dfrac{3}{13}+\dfrac{3}{13}-\dfrac{3}{14}+\dfrac{3}{14}-\dfrac{3}{15}\right)\)

\(=\dfrac{3}{1}.\left(\dfrac{3}{10}-\dfrac{3}{15}\right)\)

\(=\dfrac{3}{1}.\left(\dfrac{9}{30}-\dfrac{6}{30}\right)\)

\(=\dfrac{3}{1}.\dfrac{1}{10}\)

\(=\dfrac{3}{10}\)

A= 5/10.11+5/11.12+5/12.13+5/13.14+5/14.15

A= (1/10.11+1/11.12+1/12.13+1/13.14+1/14.15) :5

A= [(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+(1/13-1/14)+(1/14-1/15)] :5

A= (1/10-1/15):5

A= 1/30:5

A= 1/150

Ta có : (93.2727 - 9393.27).(11.12 + 12.13 + 13.14 + 14.15)

=         (93.101.27 - 9393.27).(11.12 + 12.13 + 13.14 + 14.15)

=         (9393.27 - 9393.27).(11.12 + 12.13 + 13.14 + 14.15)

=          0.(11.12 + 12.13 + 13.14 + 14.15)

=          0

Vậy ...

               Chúc các bn học giỏi ! ❤️ 

   Kb và Tk nhaaa  ♥♥!♥♥

\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(C=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(C=7\left(\frac{1}{10}-\frac{1}{70}\right)\)

\(C=7.\frac{3}{35}\)

\(C=\frac{3}{5}\)

5/10.11+5/11.12+5/12.13+5/13.14+5/14.15

=1/10-1/11+1/11-1/12+.....+1/14-1/15

=1/10-1/15

=1/30

\(=5\left(\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{14.15}\right)\)

\(5\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-...+\frac{1}{14}-\frac{1}{15}\right)\)

\(5\left(\frac{1}{10}-\frac{1}{15}\right)\)

\(=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}\)

=1/10 - 1/11+......+1/99-1/100

=1/10-1/100

=9/100

|x+3|=|-9|

TH1: x+3=9 => x=9-3                                                                       TH2: x+3=-9=> x=-9 -3

                       x=6                                                                                                  x=-12