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ta có: \(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{x}.\)
\(A=1+\frac{1}{2}+\frac{1}{2.2}+\frac{1}{2.2.2}+...+\frac{1}{x}\)
\(\Rightarrow2A=2+1+\frac{1}{2}+\frac{1}{2.2}+...+\frac{1}{x:2}\)
\(\Rightarrow2A-A=2-\frac{1}{x}\)
\(A=2-\frac{1}{x}=\frac{4095}{2048}\)
=> 1/x = 1/2048
=> x = 2048 ( 2048 = 211 )
\(2A=2+1+\frac{1}{2}+\frac{1}{4}+...+\frac{2}{x}\)
=> \(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{4}+...+\frac{2}{x}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{2}{x}+\frac{1}{x}\right)\)
=> \(A=2-\frac{1}{x}\)
Giải phương trình:
\(2-\frac{1}{x}=\frac{4095}{2048}\)
\(\frac{1}{x}=2-\frac{4095}{2048}\)
\(\frac{1}{x}=\frac{1}{2048}\)
x=2048
\(1-x=\frac{29}{12}+\frac{32}{8}\)
\(\Rightarrow1-x=\frac{77}{12}\)
\(\Rightarrow x=1-\frac{77}{12}=\frac{-65}{12}\)
\(\frac{31}{8}.x-\frac{11}{4}=\frac{42}{12}.\frac{10}{8}-\frac{1}{3}\)
\(\Rightarrow\frac{31}{8}.x-\frac{11}{4}=\frac{35}{8}-\frac{1}{3}\)
\(\Rightarrow\frac{31}{8}.x-\frac{11}{4}=\frac{97}{24}\)
\(\Rightarrow\frac{31}{8}.x=\frac{97}{24}+\frac{11}{4}=\frac{163}{24}\)
\(\Rightarrow x=\frac{163}{24}:\frac{31}{8}=\frac{163}{93}\)
Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{x\left(x+1\right):2}=\frac{399}{400}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+.....+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\left(\text{Quy đồng nhé !}\right)\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+......+\frac{2}{x\left(x+1\right)}=\frac{399}{400}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{x\left(x+1\right)}\right)=\frac{399}{400}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+.....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{399}{400}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{399}{400}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{399}{800}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{800}\)
=> x + 1 = 800
<=> x = 799
1/3+1/6+1/10+...+1/x(x+1):2=399/400
2.[1/3.2+1/6.2+1/10.2+...+1/x(x+1)]=399/400
2.[1/6+1/12+1/20+...+1/x(x+1)]=399/400
2.[1/2.3+1/3.4+1/4.5+...+1/x(x+1)]=399/400
1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=399/800
1/2-1/x+1=399/800
1/x+1=1/800
=> x+1=800
=> x=799
a, \(\left(2x-6\right)\left(x-5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=3\\x=5\end{cases}}\)
b, \(2x+\frac{1}{2}=5\)
\(2x=5-\frac{1}{2}=\frac{9}{2}\)
\(x=\frac{9}{4}\)
c, bn viết thiếu đề rồi. Nếu đề là vậy thì như này :
\(8-x+\frac{1}{5}=\frac{41}{5}-x\)
a) \(\left(2\times x-6\right)\left(x-5\right)=0\)
=> \(\orbr{\begin{cases}2\times x-6=0\\x-5=0\end{cases}}\)
=> \(\orbr{\begin{cases}2\times x=6\\x=5\end{cases}}\)
=> \(\orbr{\begin{cases}x=3\\x=5\end{cases}}\)
Vậy x = 3,x = 5
b) \(2\times x+\frac{1}{2}=5\)
=> \(2\times x=5-\frac{1}{2}\)
=> \(2\times x=\frac{9}{2}\)
=> \(x=\frac{9}{2}:2=\frac{9}{2}\cdot\frac{1}{2}=\frac{9}{4}\)
Còn câu c thiếu
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(x+x+x+x+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=1\)
\(\left(x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=1\)
\(4\times x+\frac{15}{16}=1\)
\(4\times x=1-\frac{15}{16}\)
\(4\times x=\frac{1}{16}\)
\(x=\frac{1}{16}:4\)
\(x=\frac{1}{64}\)
( x+1/2) +(1/4) + ( x + 1/8 ) + ( x + 1/6 ) = 1
x * 4 + 1/2 + 1/4 + 1/8 + 1/6 = 1
x * 4 + 1/2 + 1/4 + 1/8 = 1 - 1/6
x * 4 + 1/2 + 1/4 + 1/8 = 5/6
x * 4 + 1/2 + 1/4 = 5/6 -1/8
x * 4 + 1/2 + 1/4 = 17/24
x * 4 + 1/2 = 17/24 - 1/4
x * 4 + 1/2 = 11/24
x * 4 = 11/24 - 1/2
x * 4 = -1/24
x = -1/24 : 4
x = -1/96
Tìm X
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\)
\(=\frac{1}{5}\)
\(\Rightarrow x-100=\frac{1}{5}\)
\(x=\frac{1}{5}+100\)
\(x=\frac{1}{5}+\frac{500}{5}\)
\(x=\frac{501}{5}\)
\(x+\frac{1}{2}\times x=\frac{4}{5}\)
\(x\times\left(1+\frac{1}{2}\right)=\frac{4}{5}\)
\(x\times\frac{3}{2}=\frac{4}{5}\)
\(x=\frac{4}{5}:\frac{3}{2}\)
\(x=\frac{8}{15}\)
Vậy đáp án đúng là C
