a) Đặt A= \(\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{36}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{8}-\dfrac{1}{9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{1}{2}-\dfrac{1}{9}\)

\(\dfrac{1}{2}\)A=\(\dfrac{7}{18}\)

A=\(\dfrac{7}{9}\)

3/5+ 2/7 - 1/3

em nên gõ công thức trực quan để đề bài rõ ràng nhé

Chứng minh :

           \(S=\frac{1}{5}+\frac{1}{21}+\frac{1}{22}+...+\frac{1}{25}+\frac{1}{101}+\frac{1}{102}+...+\frac{1}{105}< \frac{1}{2}\) 

Nhóm các số hạng: 

           \(S=\frac{1}{5}+\left(\frac{1}{21}+\frac{1}{22}+...+\frac{1}{25}\right)+\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{105}\right)< \frac{1}{5}+\frac{5}{21}+\frac{5}{101}< \frac{1}{5}+\frac{5}{20}+\frac{5}{100}=\frac{1}{2}.\)

\(a,\frac{3}{17}+\frac{-5}{13}+\frac{-18}{35}+\frac{14}{17}+\frac{17}{-35}\)

=\(-\frac{5}{13}+\left(\frac{3}{17}+\frac{14}{17}\right)+\left(\frac{-18}{35}+\frac{-17}{35}\right)\)

= \(-\frac{5}{13}+1+\left(-1\right)\)

=\(-\frac{5}{13}\)

\(b,\frac{-3}{8}.\frac{1}{6}+\frac{3}{-8}.\frac{5}{6}+\frac{-10}{6}\)

=\(\frac{-3}{8}.\left(\frac{1}{6}+\frac{5}{6}\right)+\frac{-10}{6}\)

=\(\frac{-3}{8}.1+\frac{-10}{6}\)

=\(-\frac{49}{24}\)

\(c,\frac{-4}{11}.\frac{5}{15}.\frac{11}{-4}\)

=\(\left(\frac{-4}{11}.\frac{11}{-4}\right).\frac{1}{3}\)

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

\(d,\frac{13}{8}+\frac{1}{8}:\left(0,75-\frac{1}{2}\right)-25\%.\frac{1}{2}\)

=\(\frac{13}{8}+\frac{1}{8}:\left(\frac{3}{4}-\frac{1}{2}\right)-\frac{1}{4}.\frac{1}{2}\)

=\(\frac{13}{8}+\frac{1}{8}:\frac{1}{4}-\frac{1}{8}\)

=\(\frac{13}{8}+\frac{1}{2}+\frac{-1}{8}\)

=\(\left(\frac{13}{8}+\frac{-1}{8}\right)+\frac{1}{2}\)

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

\(e,\frac{-1}{2^2}-\left(-2\right)^2-5\)

=\(\frac{-1}{4}-4-5\)

=\(-\frac{37}{4}\)

\(f,\frac{121}{3}-\frac{5}{7}:\left(24-\frac{23}{57}\right)\)

=\(\frac{121}{3}-\frac{5}{7}:\frac{1345}{57}\)

=\(\frac{121}{3}-\frac{57}{1883}\)

\(\approx40,4\)

`C=(12/35-6/7+18/14):6/(-7)-(-2)/5-1`

`C=(12/35-6/7+9/7):(-6)/7+2/5-1`

`C=(12/35+3/7):(-6)/7+2/5-1`

`C=(12/35+15/35):(-6)/7+2/5-1`

`C=27/35*(-7)/6+2/5-1`

`C=-9/10+2/5-1`

`C=-9/10+4/10-1`

`C=-1/2-1=-3/2`

Ta có: \(C=\left(\dfrac{12}{35}-\dfrac{6}{7}+\dfrac{18}{14}\right):\dfrac{6}{-7}-\dfrac{-2}{5}-1\)

\(=\left(\dfrac{24}{70}-\dfrac{60}{70}+\dfrac{90}{70}\right):\dfrac{-6}{7}-\dfrac{-2}{5}-\dfrac{5}{5}\)
\(=\dfrac{27}{35}\cdot\dfrac{-7}{6}-\dfrac{3}{5}\)

\(=\dfrac{-3}{2}\)

a)  A =1 /57

b)  B = 1/41

K MIK NHA

A = 1/57

B = 1/41