\(C=2\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{61}-\frac{1}{64}\right)\)

\(C=2\cdot\left(1-\frac{1}{64}\right)\)

\(C=2\cdot\frac{63}{64}\)

\(C=\frac{63}{32}\)

Ta có : \(C=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+.........+\frac{2}{61.64}\)

\(\Rightarrow C=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+......+\frac{3}{61.64}\right)\)

\(\Rightarrow C=\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+....+\frac{1}{61}-\frac{1}{64}\right)\)

\(\Rightarrow C=\frac{2}{3}\left(1-\frac{1}{64}\right)\)

\(\Rightarrow C=\frac{2}{3}\frac{63}{64}=\frac{21}{32}\)

1)\(3x=4y\Rightarrow\frac{x}{4}=\frac{y}{3}=\frac{2x+3y}{8+9}=\frac{34}{17}=2\)

\(\Rightarrow x=4.2=8;y=2.3=6\)

2)\(\frac{x}{2}=\frac{y}{-5}=\frac{x-y}{2+5}=\frac{7}{7}=1\)

\(\Rightarrow x=2;y=-5\)

a) Ta có :

\(\frac{x}{4}=\frac{y}{3}\)

\(=\frac{2x}{8}=\frac{3y}{9}\)

Theo tính chất của dãy tỉ số bằng nhau,ta có :

\(\frac{2x}{8}=\frac{3y}{9}=\frac{2x+3y}{8+9}=\frac{34}{17}=2\)

\(\Rightarrow\hept{\begin{cases}\frac{2x}{8}=2\\\frac{3x}{9}=2\end{cases}\Rightarrow}\hept{\begin{cases}x=2.8\div2\\y=2.9\div3\end{cases}\Rightarrow\hept{\begin{cases}x=8\\y=6\end{cases}}}\)

Vậy ....
b) Theo tính chất của dãy tỉ số bằng nhau,ta có :

\(\frac{x}{2}=\frac{y}{-5}=\frac{x-7}{2-\left(-5\right)}=\frac{7}{7}=1\)

\(\Rightarrow\hept{\begin{cases}\frac{x}{2}=1\\\frac{y}{-5}=1\end{cases}\Rightarrow\hept{\begin{cases}x=1.2\\y=1.\left(-5\right)\Rightarrow\end{cases}}\hept{\begin{cases}x=2\\y=-5\end{cases}}}\)

Vậy ... 

\(9^{x-1}=\frac{1}{9}\Rightarrow9^{x-1}=9^{-1}\Rightarrow x-1=-1\Rightarrow x=0\)

\(x-3,8=-15,3-1,3x\)

\(\Rightarrow x+1,3x=-15,3+3,8\)

\(\Rightarrow2,3x=-11,5\)

\(\Rightarrow x=-11,5:2,3=-5\)

\(\frac{x+2}{7}=\frac{y-3}{5}=\frac{z}{3}=\frac{x+2+y-3-z}{7+5-3}=\frac{x+y-z-1}{9}=\frac{-17-1}{9}=-\frac{18}{9}=-2\)(t/c dãy tỉ số = nhau)

\(\Rightarrow\frac{x+2}{7}=-2\Rightarrow x+2=-2.7=-14\Rightarrow x=-14-2=-16\)

\(\Rightarrow\frac{y-3}{5}=-2\Rightarrow y-3=-2.5=-10\Rightarrow y=-10+3=-7\)

\(\Rightarrow\frac{z}{3}=-2\Rightarrow z=-2.3=-6\)

\(\frac{11}{10,5}=\frac{6,32}{x}\)\(\Rightarrow\) 11x = 10,5 . 6,32

                              11x = 66,36

                                  x = 6,032(72)

11*6,32=10,5*x=69,52

x=69,52/10,5=6,6

\(\frac{11}{10,5}=\frac{6,32}{x}\)

\(\Rightarrow11x=10,5\times6,32\)

\(\Rightarrow11x=66,36\)

\(\Rightarrow x=6,0327\)

\(\frac{11}{10,5}=\frac{6,32}{x}\Rightarrow x=\frac{6,32.10,5}{11}=\frac{1659}{275}\)

\(\frac{11}{10,5}=\frac{6,32}{x}\)

\(\Rightarrow11.x=6,32.10,5\)

\(\Rightarrow11.x=66,36\)

\(\Rightarrow x=66,36:11\)

\(\Rightarrow x=\frac{1659}{275}\)

Vậy \(x=\frac{1659}{275}.\)

Chúc bạn học tốt!

\(-13\)

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