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Answer:

\(\dfrac{1}{2}+\dfrac{2}{4}+\dfrac{3}{8}+...+\dfrac{10}{2^{10}}\)

\(=\left(\dfrac{2}{2^0}-\dfrac{3}{2^1}\right)+\left(\dfrac{3}{2^1}-\dfrac{4}{2^2}\right)+\left(\dfrac{4}{2^2}+\dfrac{5}{2^3}\right)+...+\left(\dfrac{11}{2^9}-\dfrac{12}{2^{10}}\right)\)

\(=2-\dfrac{12}{2^{10}}\)

\(=2-\dfrac{3}{256}\)

\(=\dfrac{512}{256}-\dfrac{3}{256}\)

\(=\dfrac{509}{256}\)

*Để làm bài này dễ hơn, bạn áp dụng công thức sau:

\(\dfrac{n}{2^n}=\dfrac{n+1}{2^{n-1}}-\dfrac{n+2}{2^n}\)

DD
22 tháng 4 2022

\(A=\dfrac{1}{2}+\dfrac{2}{4}+\dfrac{3}{8}+...+\dfrac{10}{2^{10}}\)

\(2A=\dfrac{1}{1}+\dfrac{2}{2}+\dfrac{3}{4}+...+\dfrac{10}{2^9}\)

\(2A-A=\left(1+\dfrac{2}{2}+\dfrac{3}{4}+...+\dfrac{10}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{2}{4}+...+\dfrac{10}{2^{10}}\right)\)

\(A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2^9}-\dfrac{10}{2^{10}}\)

\(B=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2^9}\)

\(2B=2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\)

\(2B-B=\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2^9}\right)\)

\(B=2-\dfrac{1}{2^9}\)

Suy ra \(A=B-\dfrac{10}{2^{10}}=2-\dfrac{1}{2^9}-\dfrac{10}{2^{10}}=\dfrac{509}{256}\)

17 tháng 12 2021

c: \(=\dfrac{-27\cdot100}{-30}=\dfrac{2700}{30}=90\)

21 tháng 3 2022

X = -2/5- 3/10

X= -7/10

3: \(\Leftrightarrow x\cdot\dfrac{-3}{5}=\dfrac{1}{4}+\dfrac{3}{4}=1\)

nên x=-5/3

4: \(\Leftrightarrow x\cdot\dfrac{4}{28}=\dfrac{28}{3}\cdot\dfrac{3}{28}=1\)

hay x=28/4=7

5: \(\Leftrightarrow x:\left(\dfrac{7}{2}-\dfrac{31}{6}\right)=\dfrac{21}{5}-\dfrac{20}{3}\)

\(\Leftrightarrow x:\dfrac{-5}{3}=\dfrac{-37}{15}\)

\(\Leftrightarrow x=\dfrac{37}{15}\cdot\dfrac{5}{3}=\dfrac{37}{9}\)

7 tháng 3 2022

c)\(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)....\left(1+\dfrac{1}{2020}\right)\left(1+\dfrac{1}{2021}\right)\)

\(=\left(\dfrac{1.2}{1.2}+\dfrac{1}{2}\right)\left(\dfrac{1.3}{1.3}+\dfrac{1}{3}\right)...\left(\dfrac{1.2021}{1.2021}+\dfrac{1}{2021}\right)\)

\(=\dfrac{3}{1.2}\cdot\dfrac{4}{1.3}\cdot\cdot\cdot\cdot\dfrac{2022}{1.2021}\)

\(=\dfrac{3.4.5...2022}{\left(1.1.1....1\right)\left(2.3.4...2021\right)}\)

\(=\)\(\dfrac{3.4.5...2022}{2.3.4...2021}\)

\(=\dfrac{2022}{2}=1011\)

\(d\))\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)....\left(1-\dfrac{1}{199}\right)\left(1-\dfrac{1}{200}\right)\)

\(=\left(\dfrac{2}{1.2}-\dfrac{1}{1.2}\right)\left(\dfrac{3}{1.3}-\dfrac{1}{1.3}\right)....\left(\dfrac{200}{1.200}-\dfrac{1}{1.200}\right)\)

\(=\dfrac{1.2.3....199}{\left(1.1.1....1\right).\left(2.3.4....200\right)}\)

\(=\dfrac{1.2.3...199}{2.3.4...200}\)

Nếu mik làm sai mong bạn thông cảm

7 tháng 3 2022

ý d đáp án là\(\dfrac{1}{200}\) mình quên ghi

\(=\left(\dfrac{1}{49}-\dfrac{1}{9}\right)\cdot...\cdot\left(\dfrac{1}{49}-\dfrac{1}{49}\right)\cdot...\cdot\left(\dfrac{1}{49}-\dfrac{1}{49^2}\right)=0\)

2 tháng 1 2023

2^2.3^1-(1^2021+2021^2) : (-2)

= 4.3-(1+4084441 ) : (-2)

= 12-4084442:(-2)

= 12-(-2042221)

= 20421133

Bài 2: 

a: =>2/3-x=-1/3

hay x=1

b: =>x=-2/5-2/5=-4/5

21 tháng 8

a: =>2/3-x=-1/3

hay x=1

b: =>x=-2/5-2/5=-4/5

17 tháng 1 2022

hong pé ơi =)