\(3A=\frac{3}{2.3}+\frac{3}{6.3}+\frac{1}{12.3}+\frac{3}{20.3}+\frac{3}{30.3}+\frac{3}{42.3}\)

\(3A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(3A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{7-6}{6.7}\)

\(3A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)

\(3A=1-\frac{1}{7}=\frac{6}{7}\Rightarrow A=\frac{2}{7}\)

Hình như bạn viết thiếu \(\frac{1}{36}\), nếu đúng là vậy thì mình giải như sau.

Đặt A =\(\frac{1}{6}+\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+\frac{1}{90}+\frac{1}{126}\)

3A = \(\frac{3}{3.2}+\frac{3}{3.6}+\frac{3}{3.12}+\frac{3}{3.20}+\frac{3}{3.30}+\frac{3}{3.42}\)

3A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

3A = \(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{7-6}{6.7}\)

3A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\)

3A = \(1-\frac{1}{7}=\frac{6}{7}\)

A = \(\frac{6}{7}:3=\frac{2}{7}\)

Gọi tổng là A:

ta có :

3A= 1/2+1/6+1/20+1/30+1/42

3A= 1/1.2+1/2.3+1/4.5+1/6.7

3A= 1-1/2+1/2-1/3+1/4-1/5+1/6-1/7

3A=1-1/3+1/4-1/5+1/6-1/7

3A= (1-1/7)+(1/3-1/4)+(1/5-1/7)

3A=6/7+-1/12+-2/35

3A=6/7-2/35+-1/12

3A=4/5-1/12

3A=43/60

A=43/180

Máy tính bấm auto ra ... =))

\(A=\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+...+\frac{1}{168}\)

 \(\frac{1}{3}A=\frac{1}{54}+\frac{1}{108}+...+\frac{1}{504}\)

\(\frac{1}{3}A=\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{21.24}\)

\(=\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{21}-\frac{1}{24}\)

\(=\frac{1}{6}-\frac{1}{24}\)

\(=\frac{4-1}{24}=\frac{3}{24}=\frac{1}{8}\)

=> \(A=\frac{1}{8}:\frac{1}{3}\)\(=\frac{3}{8}\)

=1/2.3+1/3.6+1/6.6+1/6.10+1/10.9+1/9.14

=1/2-1/3+1/3-1/6+1/6-1/6+1/6-1/10+1/10-1/9+1/9-1/14

=1/2-1/14

=6/14=3/7

\(\frac{1}{6}+\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+\frac{1}{90}+\frac{1}{126}\)

\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot6}+\frac{1}{6\cdot6}+\frac{1}{6\cdot10}+\frac{1}{10\cdot9}+\frac{1}{9\cdot14}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}\)

\(=\frac{1}{2}-\frac{1}{14}\)

\(=\frac{3}{7}\)

=5/18

CHO MÌNH CÁCH GIẢI VỚI Ạ  BẠN MẶC THIÊN PHONG ƠI. MÌNH CẢM ƠN

a. =(1+10)×10 :2

=11×10:2

=110:2

=55

b. Số các số hạng là =(90-9):9+1= 10

Tổng = (9+90)×10:2=495

Tự giải đi bài này mà cũng ko biết làm.

a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + \(\dfrac{8}{1}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8

=  1 + 1 + 8

=  2 + 8

= 10

b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{10}{20}\)

=  \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (\(\dfrac{2}{2}\) + \(\dfrac{3}{3}\) + \(\dfrac{4}{4}\) + \(\dfrac{5}{5}\)+ \(\dfrac{6}{6}+\dfrac{7}{7}+\dfrac{8}{8}\) + \(\dfrac{10}{10}\))

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (1 + 1 +1 + 1+ 1+ 1+ 1 +1)

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x 1 x 8

= \(\dfrac{1}{2}\) + \(\)\(\dfrac{1}{2}\) x 8

= \(\dfrac{1}{2}\) + 4

= \(\dfrac{9}{2}\)