1)

a)

\(\frac{-5}{6}.\frac{120}{25}< x< \frac{-7}{15}.\frac{9}{14}\)

\(\frac{-1}{1}.\frac{20}{5}< x< \frac{-1}{5}.\frac{3}{2}\)

\(\frac{-20}{5}< x< \frac{-3}{10}\)

\(\frac{-40}{10}< x< \frac{-3}{10}\)

\(\Rightarrow Z\in\left\{-4;-5;-6;-7;-8;-9;-10;...;-39\right\}\)

\(\left(\frac{-5}{3}\right)^3< x< \frac{-24}{35}.\frac{-5}{6}\)

\(\frac{25}{3}< x< \frac{-4}{7}.\frac{1}{1}\)

\(\frac{-25}{3}< x< \frac{-4}{7}\)

\(\frac{-175}{21}< x< \frac{-12}{21}\)

\(\Rightarrow Z\in\left\{-13;-14;-15;-16;...;-174\right\}\)

2)

a)

\(\left(\frac{9}{10}-\frac{15}{16}\right).\left(\frac{5}{12}-\frac{11}{15}-\frac{7}{20}\right)\)

\(=\left(\frac{72}{80}-\frac{75}{80}\right).\left(\frac{25}{60}-\frac{44}{60}-\frac{21}{60}\right)\)

\(=\frac{-3}{80}.\frac{-40}{60}\)

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

\(=\frac{1}{40}\)

A = 1/10 + 1/15 + 1/21 + ... + 1/120

A = 2/20 + 2/30 + 2/42 + ... + 2/240

A = 2 × (1/4×5 + 1/5×6 + 1/6×7 + ... + 1/15×16)

A = 2 × (1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/15 - 1/16)

A = 2 × (1/4 - 1/16)

A = 2 × (4/16 - 1/16)

A = 2 × 3/16

A = 3/8

lớp 5 chưa học toán này

Thế à!!!!!

a)A=1/10+1/15+...+1/120

=2(1/20+1/30+...+1/240)

=2(1/4*5+1/5*6+...+1/15*16)

=2*(1/4-1/5+1/5-1/6+...+1/15-1/16)

=2*[(1/4-1/16)+(1/5-1/5)+...+(1/15-1/15)]

=2*[(4/16-1/16)+0+...+0]

=2*3/16=3/8

b) B=1+1/3+1/6+...+1/1225

=2(1/2+1/6+1/12+...+1/2450)

=2(1/1*2+1/2*3+...+1/49*50)

=2*[1-1/2+1/2-1/3+...+1/49-1/50]

=2*[(1-1/50)+(1/2-1/2)+...+(1/49-1/49)]

=2*[(50/50-1/50)+0+...+0]

=2*49/50=49/25

a,\(\frac{1}{2}A=\frac{1}{2}\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right)\)

\(\frac{1}{2}A=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\)

\(\frac{1}{2}A=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\)

\(\frac{1}{2}A=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\)

\(\frac{1}{2}A=\frac{1}{4}-\frac{1}{16}\)\(\frac{1}{2}A=\frac{3}{16}\)suy ra \(A=\frac{3}{16}:\frac{1}{2}=\frac{3}{8}\)

B thì cậu có thể làm nhiều cách 

nkky6h njki

(1-1/15).(1-1/21).(1-1/28)...(1-1/210)          

xin loi nhung ma minh cung dang khong giai duoc cau nay, minh mong cac ban tren Online Math giup minh nhe

=(1975/1976+2010/2011+1963/1968)x(4/12-3/12-1/12)

=(1975/1976+2010/2011+1963/1968)x0

=0

a, \(\frac{2}{5}.\frac{1}{3}-\frac{2}{15}:\frac{1}{5}+\frac{3}{5}.\frac{1}{3}\)

\(=\frac{1}{3}.\left(\frac{2}{5}+\frac{3}{5}\right)-\frac{2}{15}.5\)

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

\(=\frac{1}{3}-\frac{2}{3}\)

\(=\frac{-1}{3}\)

b, \(\left(6-2\frac{4}{5}\right).3\frac{1}{8}+1\frac{3}{8}:\frac{1}{4}\)

\(=\left(6-\frac{14}{5}\right).\frac{25}{8}+\frac{11}{8}.4\)

\(=\frac{16}{5}.\frac{25}{8}+\frac{11}{2}\)

\(=10+\frac{11}{2}\)

\(=\frac{31}{2}\)

1/3×(3/5+2/5)-2/15×1/5

1/3×1-2/15×1/5

1/3-2/15×1/5

1/3-2/75

25/75-2/75

23/75

(6-14/5)×25/8-11/8:4/1

16/5×25/8-11/8:4/1

10/1-11/8:4/1

10/1-11/8×1/4

10/1-11/32

320/32-11/32

309/32

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{5.6}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\)

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

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

\(A=\frac{5}{6}\)

\(B=\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)

\(B=2.\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\right)\)

\(B=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+..+\frac{1}{15.16}\right)\)

\(B=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(B=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(B=2.\left(\frac{4}{16}-\frac{1}{16}\right)\)

\(B=2.\frac{3}{16}\)

\(B=\frac{3}{8}\)

Chúc bạn học tốt !!! 

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{5.6}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{5}-\frac{1}{6}\)

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

\(A=\frac{5}{6}\)

\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)

\(B=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(B=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)

\(B=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)

\(B=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(B=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(B=2.\frac{3}{16}\)

\(B=\frac{6}{16}=\frac{3}{13}\)

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

\(=\frac{5}{6}\)