D= 3/1 x (1/3-1/4 +1/4  -1/5+......+1/29 -1/30)

D=3 x (1/3 -1/30 )

D=3 x 3/10

D=9/10

Trời Ơi! Nhầm rùi!

Phải là 1/31 chứ

haizz..............................................

bn tinh sai oy.......

\(\frac{3}{4.5}+\frac{3}{5.6}+\frac{3}{6.7}+.....+\frac{2}{19.20}\)

\(=3.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{19.20}\right)\)

\(=3.\left(\frac{1}{4}-\frac{1}{20}\right)\)

\(=3.\frac{1}{5}=\frac{3}{5}\)

giúp mik với mik cần  gấp

Đặt \(A=\frac{3}{4.5}+\frac{3}{5.6}+\frac{3}{6.7}+..+\frac{3}{19.20}\)

\(A=3\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{19.20}\right)\)

\(A=3\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(A=3\left(\frac{1}{4}-\frac{1}{20}\right)\)

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

Ủng hộ mk nha !!! ^_^

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

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

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

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

x la nhan ha ban

a)=1

b)2 phan 3

c) 

\(C=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\)

   \(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)

   \(=\frac{1}{2}.\left(1-\frac{1}{21}\right)\)

   \(=\frac{1}{2}.\frac{20}{21}\)

   \(=\frac{10}{21}\)

\(A\)= \(\frac{1}{3.4}+\frac{1}{4.5}+..+\frac{1}{49.50}=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}=\)\(\frac{1}{3}-\frac{1}{50}=\frac{50}{150}-\frac{3}{150}=\frac{47}{150}\)

a)

 \(A=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{49.50}\)

    \(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{49}-\frac{1}{50}\)

    \(=\frac{1}{3}-\frac{1}{50}\)

    \(=\frac{47}{150}\)

b) 

 \(B=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{19.20}\)

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

    \(=3.\left(1-\frac{1}{20}\right)\)

    \(=3.\frac{19}{20}\)

    \(=\frac{57}{20}\)

\(\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+...+\frac{1}{24×25}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{5}{25}-\frac{1}{25}\)

\(=\frac{4}{25}\)

\(\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+...+\frac{1}{24\times25}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{4}{25}\)\(\left(=0,16\right)\)

\(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+......+\frac{1}{24.25}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+......+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}+\left(\frac{1}{6}-\frac{1}{6}+\frac{1}{7}-\frac{1}{7}+....+\frac{1}{25}-\frac{1}{25}\right)-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{4}{25}\)

1/5x6+1/6x7+1/7x8+...+1/2019x2020

= 6/5+7/6+8/7+...+2020/2019

Rút gọn cho nhau ta còn 2020/5=404

1/5 x 6 + 1/6 x7 + 1/7 x8 + ... + 1/2019 - 1/ 2020

=1/5 -1/6 +1/6 -1/7 + 1/7 - 1/8 + ... + 1/2019 - 1/2020

Sau khi giản ước, ta còn:

1/5 - 1/2020 = 403/2020.

                     Đáp số: 403/2020

Mình xin lôĩ, mình nhìn nhầm đề mong bạn thông cảm.

1/5×6 + 1/6×7 + 1/7×8 + ... + 1/24×25

= 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ... + 1/24 - 1/25

= 1/5 - 1/25

= 5/25 - 1/25

= 4/25

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+....+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{4}{25}\)

                         \(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{24.25}\)

                      \(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)

                     \(=\frac{1}{5}-\frac{1}{25}\) 

                   \(=\frac{5-1}{25}=\frac{4}{25}\)

                  Ủng hộ mk nha !!! ^_^