\(D=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{9}{20}\)

\(D=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{19.20}\)

\(D=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{19}-\frac{1}{20}\)

\(D=\frac{1}{2}-\frac{1}{20}\)

\(D=\frac{9}{20}\)

Vậy : . . .

HOK TỐT

1/2.3 + 1/3.4 + 1/4.5 + ... + 1/19.20

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/19 - 1/20

= 1/2 - 1/20

= 9/20

k đii

1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/19 - 1/20

1/2 - 1/20

9/20

1/2.3 + 1/3.4 + 1/4.5 + ... + 1/19.20

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/19 - 1/20

= 1/2 - 1/20

= 9/20

\(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\cdot\cdot\cdot+\dfrac{1}{18\cdot19}+\dfrac{1}{19\cdot20}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\cdot\cdot\cdot+\dfrac{1}{18}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{20}\)

\(=\dfrac{1}{2}-\dfrac{1}{20}\)

\(=\dfrac{9}{20}\)

#\(Urushi\)☕

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{9}{20}\)

Ta có công thức :\(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{19.20}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{9}{20}\)

Ta có :

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}=\frac{10}{20}-\frac{1}{20}=\frac{9}{20}\)

Vậy tổng \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}=\frac{9}{20}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{18}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{20}\)

=1-1/20

=19/20

\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{19\cdot20}\)

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

\(=1-\dfrac{1}{20}=\dfrac{19}{20}\)

\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+....+\dfrac{1}{19\cdot20}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+....+\dfrac{1}{19}-\dfrac{1}{20}\)

\(A=1-\dfrac{1}{20}\)

\(A=\dfrac{19}{20}\)

Trả lời

a) \(\frac{-2}{2\cdot3}+\frac{-2}{3\cdot4}+\frac{-2}{4\cdot5}+...+\frac{-2}{19\cdot20}\)

\(=-2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{19\cdot20}\right)\)

\(=-2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(=-2\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=-2\cdot\frac{9}{20}\)

\(=\frac{-18}{20}=\frac{-9}{10}\)

.3-2/2.3 + 4-3/3.4 + 5-4/4.5 + 6-5/5.6 +...+ 20-19/19.20=18/x

1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 +...+ 1/19 - 1/20=18/x

1/2 - 1/20=18/x

10/20 - 1/20=18/x

9/20=18/x

18/40=18/x

=>x=40

Vậy x=40

Thanks

A= 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6

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

A= 1/2- 1/6

A= 1/3

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)

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

\(\Rightarrow A=\frac{1}{2}-\frac{1}{6}\)

\(\Rightarrow A=\frac{1}{3}\)

Wa cảm ơn các bạn nhiều nha