\(\left(1-\dfrac{1}{10}\right):\left(1+\dfrac{1}{10}\right):\left(1+\dfrac{1}{11}\right):\left(1+\dfrac{1}{12}\right):...:\left(1+\dfrac{1}{500}\right)\)

=\(\dfrac{9}{10}:\dfrac{11}{10}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)

=\(\dfrac{9}{10}.\dfrac{10}{11}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)

=\(\dfrac{9}{11}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)=\(\dfrac{9}{501}\)=\(\dfrac{3}{167}\)

-Mình làm rồi. Bạn xem bài đăng lúc nãy của bạn,

3/167

a: \(\dfrac{-1}{2}+\dfrac{5}{6}+\dfrac{1}{3}\)

\(=\dfrac{-3}{6}+\dfrac{5}{6}+\dfrac{2}{6}\)

\(=\dfrac{4}{6}=\dfrac{2}{3}\)

b: \(\dfrac{-3}{8}+\dfrac{7}{4}-\dfrac{1}{12}\)

\(=\dfrac{-9}{24}+\dfrac{42}{24}-\dfrac{2}{24}\)

\(=\dfrac{31}{24}\)

c: \(\dfrac{3}{5}:\left(\dfrac{1}{4}\cdot\dfrac{7}{5}\right)=\dfrac{3}{4}:\dfrac{7}{20}=\dfrac{3}{4}\cdot\dfrac{20}{7}=\dfrac{15}{7}\)

d: \(\dfrac{10}{11}+\dfrac{4}{11}:4-\dfrac{1}{8}\)

\(=\dfrac{10}{11}+\dfrac{1}{11}-\dfrac{1}{8}=\dfrac{7}{8}\)

=1140,281042

\(\text{A = 1-2-3-4+5-6-7-8+9-10-11-12+...........+97-98-99-100}\)

\(\text{A =(1-2-3-4)+(5-6-7-8)+(9-10-11-12)+.............+(97-98-99-100)}\)

\(\text{A =-8+(-16)+(-24)+..................+(-200)}\)

\(\text{A =-8.(1+2+3+......+25)}\)

\(\text{A =-8.[(25-1):1+1.26:2]}\)

\(\text{A =-8.325}\)

\(\text{A =-2600 Vậy A = -2600 }\)

=1+(2-3-4+5)+(6-7-8+9)+...+(98-99-100+101)+102
=1+0+0+0+....+102
=103

k mk nha

ne bang 153 dung khong nhi 

153 ddddo

Ta có :

\(A=\dfrac{10^{11}-1}{10^{12}-1}< 1\)

\(\Leftrightarrow A< \dfrac{10^{11}-1+11}{10^{12}-1+11}=\dfrac{10^{11}+10}{10^{12}+10}=\dfrac{10\left(10^{10}+1\right)}{10\left(10^{11}+1\right)}=\dfrac{10^{10}+1}{10^{11}+1}=B\)

Vậy \(\dfrac{10^{11}-1}{10^{12}-1}< \dfrac{10^{10}+1}{10^{11}+1}\)

Vậy...

Vì \(10^{11}-1< 10^{12}-1\)

\(\Rightarrow\dfrac{10^{11}-1}{10^{12}-1}< \dfrac{10^{11}-1+11}{10^{12}-1+11}=\dfrac{10^{11}+10}{10^{12}+10}=\dfrac{10^{10}+1}{10^{11}+1}\)