tính hộ mình nha

\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{15.16}\)

\(\left(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\right).\frac{1}{x}=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{15.16}\right)\)

\(\frac{8+4+2+1}{16}.\frac{1}{x}=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(\frac{15}{16}.\frac{1}{x}=3.\left(1-\frac{1}{16}\right)\)

\(\frac{15}{16}.\frac{1}{x}=3.\frac{15}{16}\)

=> \(\frac{1}{x}=3\)

=> \(x=\frac{1}{3}\)

1 + 1 =  2

2 + 3= 5

6 + 6 = 12  

Tìm x:

X + 3,68 = 4,035

X           = 4,035 - 3,68

X           = 0,355

5,0165 : X = 5

            X  = 5,0165 : 5

            X = 1,0033

Ủng hộ nha! :)      

Bài 1 :

1 + 1 = 2

2 + 3 = 5

6 + 6 = 12

Bài 2 :

x + 3,68 = 4,035

x           = 4,035 - 3,68

x            = 0,35

5,0165 : x = 5

              x = 5,0165 : 5

              x = 1.0033

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{\left(x-1\right)\times x}=\frac{15}{16}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x-1}-\frac{1}{x}=\frac{15}{16}\)

\(1-\frac{1}{x}=\frac{15}{16}\)

\(\frac{1}{x}=\frac{1}{16}\)

\(\Rightarrow x=16\)

\(\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x...x\left(1-\frac{1}{2014}\right)\)

A = \(\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{2012}{2013}x\frac{2013}{2014}\)

A = \(\frac{2x3x4x...x2012x2013}{3x4x5x...x2013x2014}\)

a = \(\frac{2}{2014}=\frac{1}{1007}\)

1/1007 do

Áp dụng công thức: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

Ta có:

VT=\(x-\left(\left(1-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{3}\right)-...\left(\frac{1}{98}-\frac{1}{99}\right)-\left(\frac{1}{99}-\frac{1}{100}\right)\right)\)

=\(x-\frac{1}{100}\)

Dễ dàng tìm được 

\(x-\frac{1}{100}=\frac{1}{100}\) 

\(x=\frac{1}{50}\)

\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\)

\(=\)\(\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\)

\(=\)\(\frac{9}{3}\)

\(=\)\(3\)

\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}\)

\(=\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\)

Rút gọn phép tính trên ta được :

\(=\frac{9}{3}=3\)

Haaa

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\(x\times2+x\times\frac{1}{5}=1\frac{3}{5}\)

\(x\times\left(2+\frac{1}{5}\right)=\frac{8}{5}\)

\(x\times\frac{11}{5}=\frac{8}{5}\)

\(x=\frac{8}{5}\div\frac{11}{5}\)

\(x=\frac{8}{11}\)

\(\Rightarrow x.\left(2+\frac{1}{5}\right)=\frac{8}{5}\)

\(\Rightarrow\frac{11}{5}x=\frac{8}{5}\)

\(\Rightarrow x=\frac{8}{11}\)