\(\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{20\times21}=\dfrac{x}{14}\)

\(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{20}-\dfrac{1}{21}=\dfrac{x}{14}\)

\(\dfrac{1}{3}-\dfrac{1}{21}=\dfrac{x}{14}\)

\(\dfrac{7}{21}-\dfrac{1}{21}=\dfrac{x}{14}\)

\(\dfrac{6}{21}=\dfrac{x}{14}\)

\(\Rightarrow x.21=6.14\)

\(x.21=84\)

\(x=84:21\)

\(x=4\)

Vậy x = 4

1/3x4 + 1/4x5 + 1/5x6 + .. + 1/20x21 = x/14

1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + .. + 1/20 - 1/21 = x/14

1/3 - 1/21 = x/14

7/21 - 1/21 = x/14

6/21 = x/14

x . 21 = 6 x 14

x x 21 = 84

x = 84 : 21

x = 4

1/(3×4) + 1/(4×5) + 1/(5×6) + ... + 1/(20×21) = x/14

1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/20 - 1/21 = x/14

1/3 - 1/21 = x/14

2/7 = x/14

x = 14 × 2/7

x = 4

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{6}-\dfrac{1}{7}=\dfrac{1}{2}-\dfrac{1}{7}=\dfrac{5}{14}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{20}-\dfrac{1}{21}=\dfrac{21-2}{42}=\dfrac{19}{42}\)

Lời giải:
Gọi biểu thức số 1 là A và số 2 là B

\(A=\frac{3-2}{2\times 3}+\frac{4-3}{3\times 4}+\frac{5-4}{4\times 5}+\frac{6-5}{5\times 6}+\frac{7-6}{6\times 7}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)

B tương tự A:
\(B=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{20}-\frac{1}{21}\)

\(=\frac{1}{2}-\frac{1}{21}=\frac{19}{42}\)

\(A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}=\dfrac{1}{2}-\dfrac{1}{8}=\dfrac{3}{8}\)

=1+1/3-1/4+1/4-1/5+1/5-1/6

=4/3-1/6=7/6

Đợi nhé

Bài nào khó lắm thì mới hỏi thôi chứ bài này dễ mà bạn tự vận động não đi

\(\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{11\cdot12}=x\)

\(\Leftrightarrow x=\dfrac{1}{3}-\dfrac{1}{12}=\dfrac{4}{12}-\dfrac{1}{12}=\dfrac{1}{4}\)

dễ lắm ko cần hỏi đâu ,tự vận động não đi

=1+1/3-1/4+1/4-1/5+1/5-1/6

=1+1/3-1/6

=1+1/6=7/6

nhanh lên mọi người ơi , mình đang vội☹

1/1x2 + 1/2x3 + 1/3x4 +1/4x5 +1/5x6

= 1 -1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6

= 1 - 1/6 = 5/6

=\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{11}-\frac{1}{12}\)

=\(\frac{1}{3}-\frac{1}{12}\)

=\(\frac{3}{12}=\frac{1}{4}\)

\(\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{11\times12}\)                                                                                                  =\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)                                                                          =\(\frac{1}{3}-\frac{1}{12}\)                                                                                                                                                   =\(\frac{1}{4}\)

Ta có : 1/2.3+1/3.4+1/4.5+1/5.6

=1/2-1/3+1/3-1/4+….+1/5-1/6

=1/2-1/6

=2/6=1/3

\(\frac{1}{2x3}\) + \(\frac{1}{3x4}\) + \(\frac{1}{4x5}\) + \(\frac{1}{5x6}\)

=\(\frac{1}{2}\) -\(\frac{1}{3}\) +\(\frac{1}{3}\) -\(\frac{1}{4}\) +\(\frac{1}{4}\) -\(\frac{1}{5}\) +\(\frac{1}{5}\) -\(\frac{1}{6}\)

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

k cho mình nha