S= 1/2 + 1/6 + 1/12 + ...+ 1/90

S=1/1.2 + 1/2.3 +1/3.4+...+1/9.10

S=1-1/2 + 1/2-1/3 + 1/3-1/4+...+1/9-1/10

S=(1-1/10)+(1/2-1/2)+(1/3-1/3)+...+(1/9-1/9)

S=9/10+0+0+...+0

S=9/10Chúc bn học tốt =))

1/2+1/6+1/12+1/20+1/30+...+1/90=

1/1*2+1/2*3+1/3*4+...+1/9*10=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10=

1/1-1/10=9/10 ban a

1/2+1/6+1/12+1/20+1/30+...+1/90

=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+...+1/9.10

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10

=1-1/10

=9/10

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}\)

\(=\frac{9}{10}\)

k nha

A=\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+......+\(\frac{1}{9.10}\)

A=\(\frac{1}{1}\)-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+........+\(\frac{1}{9}\)-\(\frac{1}{10}\)

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

Mơn thím nhìu

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}\)

\(=\frac{9}{10}\)

Đề sai hả bạn

sau đây là phần chữa của mình: 

\(=\dfrac{1}{2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}\)

\(=\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

 \(=\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{10}\)

= \(\dfrac{3}{10}\)

= \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

= \(\dfrac{1}{2}-\dfrac{1}{10}\)

= \(\dfrac{2}{5}\)

chỗ đầu mình quên cộng thêm 1/2 rồi bạn nhớ bổ sung nha thì sẽ ra kết quả đúng nhé

A = \(3-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-...-\frac{1}{90}\)

A = \(\frac{1}{3}-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-...-\frac{1}{90}\)

A = \(\frac{1}{3}-\frac{1}{1}-\frac{1}{1}-\frac{1}{1}-\frac{1}{5}-...-\frac{1}{90}\)

A = \(\frac{1}{3}-\frac{1}{90}\)

A = \(\frac{29}{90}\)

tại sao 3==1/3

= 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + ...... + 1/9x10

= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4-1/5 +.......+ 1/9 -1/10

= 1/1 - 1/10

= 9/10

=1/1x2+1/2x3+1/3x4+1/4x5+......+1/9x10

89/90 Đấy

89/90

T=1/2+1/6+1/12+1/20+1/30+...+1/72+1/90

=> T=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+...+1/9.10

=> T=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10

=> T=1/1-1/10

=> T=9/10