1/3+1/6+1/10+...+1/x(x+1)=1 2013/2015
(kết quả là hỗn số 1 2013 phân 2015)
Những câu hỏi liên quan
tìm số tự nhiên x biết : 1/3+1/6+1/10+...+2/ x(x+1)=2013/2015
tìm số tự nhiên x biết : 1/3 + 1/6 +1/10 + .....+2/x(x+1) =2013/2015
=>2/6+2/12+2/20+...+2/x(x+1)=2013/2015
=>2(1/2.3+1/3.4+1/4.5+...+1/x(x+1)=2013/2015
=>2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1)=2013/2015
=>(1/2-1/x+1)=2013/2015:2
=>-(1/x+1)=2013/4030-1/2
=>-(1/x+1)=-(1/2015)=>x+1=2015=>x=2014
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2 tháng 4 2015 lúc 11:30
tìm số tự nhiên x biết: 1/3+1/6+1/10+...+2/x(x+1)=2013/2015
\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\cdot\left(x+1\right)}=\frac{2013}{2015}\)
\(\Rightarrow2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{x\cdot\left(x+1\right)}\right)=\frac{2013}{2015}\)
\(\Rightarrow2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{x\cdot\left(x+1\right)}\right)=\frac{2013}{2015}\)
\(\Rightarrow2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2013}{2015}\)
\(\Rightarrow\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2013}{2015}:2\)
\(\Rightarrow-\frac{1}{x+1}=\frac{2013}{4030}-\frac{1}{2}\)
\(\Rightarrow-\frac{1}{x+1}=-\frac{1}{2015}\Rightarrow x+1=2015\Rightarrow x=2014\)
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Xem thêm câu trả lời
Tìm x biết: 1/3+1/6+1/10+...+1/x(x+1):2=2013/2015
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2013}{2015}:2\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{4030}\)
tự làm tiếp nhé mk ăn cơm đã
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Tìm x thuộc Z biết 1/3+1/6+1/10+...+1/x(x+1)=2013/2015
2/6+2/12+2/20+...+2/x(x+2)=2013/2015
2(1/2.3+1/3.4+...+1/x(x+1))=2013/2015
2(1/2-1/3+1/3-1/4+...+1/x-1/x+1)=2013/2015
2(1/2-1/x+1)=2013/2015
1/2-1/x+1=2013/2015:2
1/2-1/x+1=2013/4030
1/x+1=1/2-2013/4030
1/x+1=1/2015
Suy ra x+1=2015
x=2014
Vậy x=2014
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cho a=1/3+1/6+1/10+....+2/x (x+1) =2013/2015
tinh x
\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\)
\(\Rightarrow A=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\)
\(\Rightarrow A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\)
\(\Rightarrow A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2013}{2015}\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{2015}:2\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2013}{4050}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2015}\)
=> x + 1 = 2015
=> x = 2014
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1/1*3 + 1/3*5 + 1/5*7 + ... + 1/2013*2015 =1/2 - 1/x
các số trên đều là phân số
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{2013.2015}=\frac{1}{2}-\frac{1}{x}\)
\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)=\frac{1}{2}-\frac{1}{x}\)
\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{2015}\right)=\frac{1}{2}-\frac{1}{x}\)
\(\Leftrightarrow\frac{1}{2}\cdot\frac{2014}{2015}=\frac{1}{2}-\frac{1}{x}\)
\(\Leftrightarrow\frac{1007}{2015}=\frac{1}{2}-\frac{1}{x}\)
\(\Leftrightarrow\frac{1}{x}=\frac{1}{2}-\frac{1007}{2015}\Leftrightarrow\frac{1}{x}=\frac{1}{4030}\)
\(\Rightarrow x=4030\)
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tính nhanh
A=1+3-5+7-..........-2013+2015
B=1-2+3-4+...................2015-2016
C=1-2-3+4+5-6-6+8+...........+2013-2014-2015+2016
D=1-4+7-10+.....-2014+2017
E=1+2-3-3+5+6 -.......+2013+2014-2015-2016
F=1-2+3-4+..........+2015+2016
G=1+3-5-7+9+11.............-2013-2015
H=1-2-34+5-6-7+8+.................+1013-1014-1015+1016
chị kết bạn với em nha gửi lời kết bn với em nhé
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\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)}=1\frac{2013}{2015}\)