\(B=\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}\)

\(B=\frac{-5}{1.3}+\frac{-5}{3.5}+\frac{-5}{5.7}+...+\frac{-5}{49.51}\)

\(B=\frac{-5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\right)\)

\(B=\frac{-5}{2}.\left[\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{51}\right)\right]\)

\(B=\frac{-5}{2}.\left[1-\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{49}\right)-\frac{1}{51}\right]\)

\(B=\frac{-5}{2}.\left(1-\frac{1}{51}\right)=\frac{-5}{2}.\frac{50}{51}=\frac{-125}{51}\)

=-5/1.3+-5/3.5+-5/5.7+.............+-5/49.51

-5/2(1-1/51)

=-125/51

ai k mk mk k lai

ok

B = -5/1.3 + -5/3.5 +.....+ -5/49.51

B = -5/2(1 - 1/51)

B = -5/2 . 50/51

B = -125/51 nha!

a)\(\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{100.103}=\frac{5}{3}\cdot\left(\frac{3}{1.4}+\frac{4}{4.7}+...+\frac{3}{100.103}\right)\)

\(=\frac{5}{3}\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{100}-\frac{1}{103}\right)=\frac{5}{3}\cdot\left(1-\frac{1}{103}\right)=\frac{5}{3}\cdot\frac{102}{103}=\frac{170}{103}\)b)\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)

\(\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{51}\right)=\frac{1}{2}\cdot\frac{16}{51}=\frac{8}{51}\)

Câu a) bạn Ác Mộng làm rồi nên mình làm b) nha

b)Gọi A = \(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}\)

\(A=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)

\(2A=2.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\right)\)

\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\)

\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)

\(2A=\frac{1}{3}-\frac{1}{51}\)

\(2A=\frac{16}{51}\)

\(A=\frac{16}{51}:2\)

\(A=\frac{8}{51}\)

5*(5-5/4+5/4-5/7+.......+5/100-5/103)

5*(5-5/103)

5*......... bạn tự tính nhé

câu b 1/3*5+1/5*7+............+1/49*51

1*(1/1-1/3+1/3-1/5+............+1/49-1/51)

1/1-1/51 tính ra rồi ra kết quả

tk nha

\(a,=\left(\frac{15}{12}-\frac{3}{12}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)\)

\(=1+-1\)

\(=0\)

a) \(\frac{{ - 3}}{7}.\frac{2}{5} + \frac{2}{5}.\left( { - \frac{5}{{14}}} \right) - \frac{{18}}{{35}}\)

\(\begin{array}{l} = \frac{2}{5}.\left( {\frac{{ - 3}}{7} + \frac{{ - 5}}{{14}}} \right) - \frac{{18}}{{35}}\\ = \frac{2}{5}.\left( {\frac{{ - 6}}{{14}} + \frac{{ - 5}}{{14}}} \right) - \frac{{18}}{{35}}\\ = \frac{2}{5}.\frac{{ - 11}}{{14}} - \frac{{18}}{{35}} = \frac{{ - 11}}{{35}} - \frac{{18}}{{35}} =  \frac{{ -29}}{{35}}\end{array}\)

b) \(\left( {\frac{2}{3} - \frac{5}{{11}} + \frac{1}{4}} \right):\left( {1 + \frac{5}{{12}} - \frac{7}{{11}}} \right)\)

\(\begin{array}{l} = \left( {\frac{{2.11.4}}{{3.11.4}} - \frac{{5.3.4}}{{11.3.4}} + \frac{{1.3.11}}{{4.3.11}}} \right):\left( {\frac{11.12}{11.12} + \frac{{5.11}}{{12.11}} - \frac{{7.12}}{{11.12}}} \right)\\ = \left( {\frac{{88 - 60 + 33}}{{121}}} \right):\left( { \frac{{121+55 - 84}}{{121}}} \right)\\ = \frac{{61}}{{121}}:\frac{{92}}{{121}} = \frac{{61}}{{121}}.\frac{{121}}{{92}}= \frac{{61}}{{92}}\end{array}\)

c) \(\left( {13,6 - 37,8} \right).\left( { - 3,2} \right)\)

\( = \left( { - 24,2} \right).\left( { - 3,2} \right) = 77,44\)

d) \(\left( { - 25,4} \right).\left( {18,5 + 43,6 - 16,8} \right):12,7\)

\(\begin{array}{l} = \left( { - 25,4} \right).\left( {62,1 - 16,8} \right):12,7\\ = \left( { - 25,4} \right).45,3:12,7\\ = \left( { - 25,4} \right):12,7.45,3\\ =  (- 2).45,3 =  - 90,6\end{array}\)

a: \(=\dfrac{2}{5}\cdot\left(-\dfrac{3}{7}-\dfrac{5}{14}\right)-\dfrac{18}{35}\)

\(=\dfrac{2}{5}\cdot\dfrac{-6-5}{14}-\dfrac{18}{35}\)

\(=\dfrac{2}{5}\cdot\dfrac{-11}{14}-\dfrac{18}{35}=-\dfrac{22}{70}-\dfrac{18}{35}=\dfrac{-58}{70}=-\dfrac{29}{35}\)

b: \(=\dfrac{88-60+33}{132}:\dfrac{132+55-84}{132}\)

\(=\dfrac{61}{132}\cdot\dfrac{132}{103}=\dfrac{61}{103}\)

c: \(=-24.2\cdot\left(-3.2\right)=24.2\cdot3.2=77.44\)

d: \(=\dfrac{-25.4}{12.7}\cdot45.3=-2\cdot45.3=-90.6\)

\(\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)

\(=\frac{\frac{1}{2}.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{8}\right)}{5\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{8}\right)}\)

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

Study well 

2/5 nhé bạn!

Có người vẫn chưa hiểu bản chất của phép tính à 

\(\frac{\frac{1}{2}}{5}\)

\(=\frac{1}{2}:5\)

\(=\frac{1}{2}.\frac{1}{5}\)

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

giờ hiểu chứ 

\(a.=\frac{3}{15}+\frac{-10}{15}\)

\(=-\frac{7}{15}\)

\(b.=\left(\frac{15}{12}-\frac{3}{12}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)\)

\(=1+\left(-1\right)\)

\(=0\)

\(c.=\left(\frac{13}{25}-\frac{38}{25}\right)+\left(\frac{6}{41}+\frac{35}{41}\right)-\frac{1}{2}\)

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

\(=0-\frac{1}{2}\)

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

\(d.=\frac{5}{6}.\left(18\frac{2}{3}-6\frac{2}{3}\right)\)

\(=\frac{5}{6}.12\)

\(=10\)

a)1/5+-2/3

=3/15+-10/15

=-7/15

b)15/12+5/13-3/12-18/13

=(15/12-3/12)+(5/13-18/13)

=1+-1

=0

c)13/25+6/41-38/25+35/41-1/2

=(13/25-38/25)+(6/41+35/41)-1/2

=1+1-1/2

=2-1/2

=2/2-1/2

=1/2

d)5/16x18’2/3-5/6x6’2/3

=5/16x(18’2/3-6’2/3)

=5/16x12

=15/4

Chúc bạn hok tốt😄😄

\(M=\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}\)

\(\Rightarrow M=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)

\(\Rightarrow2M=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\)

\(\Rightarrow2M=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)

\(\Rightarrow2M=\frac{1}{3}-\frac{1}{51}\)

\(\Rightarrow2M=\frac{16}{51}\)

\(\Rightarrow M=\frac{8}{51}\)

\(N=\frac{-5}{1.3}+\frac{-5}{3.5}+...+\frac{-5}{2013.2015}\)

\(\Rightarrow N=-\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2013.2015}\right)\)

\(\Rightarrow N=-\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)

\(\Rightarrow N=-\frac{5}{2}\left(1-\frac{1}{2015}\right)\)

\(\Rightarrow N=-\frac{5}{2}.\frac{2014}{2015}\)

\(\Rightarrow N=-\frac{1007}{403}\)