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

\(=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{10-9}{9.10}\)

\(=\frac{3}{2.3}-\frac{2}{2.3}+\frac{4}{3.4}-\frac{3}{3.4}+...+\frac{10}{9.10}-\frac{9}{9.10}\)

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

\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)

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

=1-1/10

=10/10-1/10

=9/10

Bài làm:

  \(\frac{1}{1\times2}+\frac{1}{2\times3}\)\(+\frac{1}{3\times4}+\frac{1}{4\times5}\)\(+...\frac{1}{9\times10}\)

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

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

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

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

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

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

\(=\frac{2}{5}\)

\(\frac{1}{1x2}+\frac{1}{2x3}+...+\frac{1}{9x10}\)

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

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

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

= 9/10

k nha

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

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

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

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

chúc bn học tốt

\(1,27+2,77+4,27+5,77+...+31,27+32,47\)

\(=\left(1,27+32,77\right)+\left(2,77+31,27\right)+....+\left(16,27+17,77\right)\)

\(=34,04+34,04+....+34,04\)( 11 số hạng)

\(=34,04.11=374,44\)

chúc bn học tốt

=330

ủng hộ mk nhé

330 là kết quả đúng đó bạn!

\(1.2+2.3+3.4+4.5+...+9.10\)

Đặt A = \(1.2+2.3+3.4+4.5+...+9.10\)

\(3.A\) = \(1.2.3+2.3.3+3.4.3+4.5.3+...+9.10.3\)

=> \(3.A\) = \(1.2.3+2.3.4+3.4.5+4.5.6+...+9.10.11\)

Ta có: \(3.A=9.10.11\)

=>: \(A=\frac{9.10.11}{3}=330\)

=> A = 330 

2+6+12+20+30+42+56+72+90=330

1/1 x 2 + 1/2 x 3 + 1/3 x 4 + .... + 1/9 x 10

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

= 1 - 1/10

= 9/10

\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{9\times10}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\\ =1-\dfrac{1}{10}\\ =\dfrac{9}{10}\)

Ta đặt biểu thức là:

A = 1/1 x 2 + 1/2 x 3 + 1/3 x 4 + .... + 1/9 x 10

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

A = 1 - 1/10

A = 9/10

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

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

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