\(B=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{98.99}\)

\(=\dfrac{2-1}{1.2}+\dfrac{3-2}{2.3}+\dfrac{4-3}{3.4}+...+\dfrac{99-98}{98.99}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{98}-\dfrac{1}{99}\)

\(=1-\dfrac{1}{99}\)

\(A=\dfrac{2021}{2022}=\dfrac{2022-1}{2022}=1-\dfrac{1}{2022}\)

Có \(2022>99>0\Leftrightarrow\dfrac{1}{99}>\dfrac{1}{2022}\)

Suy ra \(A>B\).

Ta có : A = 1/1.2 + 1/2.3 + .... + 1/98.99 + 1/99.100 .

=>       A = 1 - 1/2 + 1/2 - 1/3 + .... + 1/98 - 1/99 + 1/99 - 1/100 .

=>       A = 1 - 1/100 .

=>       A = 99/100 .

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow A=1-\frac{1}{100}\)

\(\Rightarrow A=\frac{99}{100}\)

Cảm ơn nhìu nha

Đặt A=1.98+2.97+3.96+...+96.3+97.2+98.1

       B=1.2+2,3+3.4+...+96.97+97.98+98.99

Ta có: A=1+(1+2)+...+(1+2+3+...+97+98)

              =\(\dfrac{1.2}{2}+\dfrac{2.3}{2}+...+\dfrac{98.99}{3}\)

              =\(\dfrac{1.2+2.3+3.4+4.5+...+98.99}{2}\)=\(\dfrac{B}{2}\)

    =>E=\(\dfrac{B}{2}\):2=\(\dfrac{1}{2}\)

...

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

= 1/2-1/20

=9/20

có phải như thế này ko bn

\(A=\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{19.20}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{19}-\frac{1}{20}=\frac{1}{2}-\frac{1}{20}\)

A = \(\frac{9}{20}\)

\(B=\frac{1}{99.100}-\frac{1}{98.99}-\frac{1}{97.98}-.....-\frac{1}{1.2}=-\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{99.100}\right)\)

\(B=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\right)=-\left(1-\frac{1}{100}\right)\)

B = \(-\frac{99}{100}\)

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

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

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

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

Tương tự với ý B

Đặt tổng trên = A

Có : 3A = 1.2.3+2.3.3+....+98.99.3

 = 1.2.3+2.3.(4-1)+.....+98.99.(100-97)

 = 1.2.3+2.3.4-1.2.3+.....+98.99.100-97.98.99

 = 98.99.100

=> A = 98.99.100/3 = 323400

k mk nha

Gọi A = 1.2 + 2.3 + .. + 98.99

3A = 1.2.3 + 2.3.3 + ... + 98.99.3

3A = 1.2.3 + 2.3.(4 - 1) + ... + 98.99.(100 - 97)

3A = 1.2.3 + 2.3.4 - 1.2.3 + ... + 98.99.100 - 97.98.99

3A = 98.99.100

3A = 970200

A = 323400

đặt A = 1.2 + 2.3 + 3.4 + ... + 97.98 + 98.99

3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 97.98.3 + 98.99.3

3A = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + ... + 97.98.(99-96) + 98.99.(100-97)

3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 97.98.99 - 96.97.98 + 98.99.100 - 97.98.99

3A = 98.99.100

A = 98,99.100 : 3

A = 333300