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S=1/2+1/2^2+...+1/2^2019
2S=1+1/2+...+1/2^2018
=> 2S-S=1-1/2^2019
=>S=1-1/2^2019<1
VậyS<1
a) \(\frac{X}{2}-\frac{11}{5}=\frac{7}{8}\cdot\frac{64}{49}\)
\(\Rightarrow\frac{x}{2}-\frac{11}{5}=\frac{8}{7}\)
\(\Rightarrow\frac{x}{2}=\frac{8}{7}+\frac{11}{5}\)
\(\Rightarrow\frac{x}{2}=\frac{117}{35}\)\(\Rightarrow x=\frac{117}{35}\cdot2=\frac{234}{35}\)
b)\(\frac{x}{5}+\frac{9}{2}=\frac{6}{7}\cdot\frac{36}{49}\)
\(\Rightarrow\frac{x}{5}+\frac{9}{2}=\frac{216}{343}\)
\(\Rightarrow\frac{x}{5}=\frac{216}{343}-\frac{9}{2}=\frac{-2655}{686}\)
\(\Rightarrow x=\frac{-2655}{686}\cdot5=\frac{-13275}{686}\)
x/2 - 11/5 = 7/8 . 64/49
x/2 - 11/5 = 8/7
x/2 =8/7 + 11/5
x/2 = 117/35
x = 2.117/35 ( tính chất phân số bằng nhau)
x = 234/35
x/5 + 9/2 = 6/7 . 36/49
x/5 + 9/2 = 216/343
x/5 = 216/343 - 9/2
x/5 = -2655/686
x = 5.(-2655)/686
x = -13275/686
Vi cong them n vao tu va tru n o mau nen tong cua tu so va mau so khong doi . Khi do tong tu va mau so cua PS moi la : 37+99=136 .
PS moi =3/5 va tong tu mau la 136 ban ve so do va giai theo cach tong va ti thi ra phan so moi (51/83) . Tru di ta duoc n =14
\(\frac{x}{3\frac{1}{2}.2\frac{2}{3}}=\frac{9}{56}\Rightarrow\frac{x}{\frac{7}{2}.\frac{8}{3}}=\frac{9}{56}\Rightarrow x=\frac{9}{56}.\frac{28}{3}=\frac{3}{2}\)
\(x:\left(3\frac{1}{2}.2\frac{2}{3}\right)=\frac{9}{56}\)
\(x:\left(\frac{7}{2}.\frac{8}{3}\right)=\frac{9}{56}\)
\(x:\left(\frac{7.4}{3}\right)=\frac{9}{56}\)
\(x.\frac{3}{28}=\frac{9}{56}\)
\(x=\frac{9}{56}.\frac{28}{3}=\frac{3}{2}\)
Vậy \(x=\frac{3}{2}\)
A=1/1.2+1/2.3+...1/x =49/50
A=1-1/2+1/2-1/3+...+1/x-1-1/x=49/50
A=1-1/x=49/50
A=50/50-1=x=49/50
x=1/50
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{x}=\frac{49}{50}\)
\(\Rightarrow\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{x\left(x-1\right)}=\frac{49}{50}\)
\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x-1}-\frac{1}{x}=\frac{49}{50}\)
\(\Rightarrow1-\frac{1}{x}=\frac{49}{50}\)
\(\Rightarrow\frac{1}{x}=\frac{1}{50}\)
\(\Rightarrow x=50\)