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cách này ngon hơn nè
\(2A=2\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)
\(2A=2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\)
\(2A-A=\left(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)
\(A=2-\frac{1}{2^{2012}}\)
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Ta có : \(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)x=\frac{2012}{1}+\frac{2011}{2}+...+\frac{1}{2012}\)(sửa lại đề)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)x=1+\left(\frac{2011}{2}+1\right)+...+\left(\frac{1}{2012}+1\right)\)(2012 số hạng 1)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)x=1+\frac{2013}{2}+...+\frac{2013}{2012}\)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right)x=2013\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right)\)
=> x = 2013
Vậy x = 2013
(1+2012/1)(1+2012/2)(1+2012/3).......(1+2012/1000)
(1+1000/1)(1+1000/2)..........(1+1000/2012)
Tính A
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\(A=\frac{\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+...+\frac{1}{2012}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}}\)'
\(A=\frac{\left(1+\frac{2012}{2}+1+\frac{2010}{2}+1+...+\frac{1}{2012}+1\right)}{\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}\right)}\)
\(A=\frac{\left(1+\frac{2013}{2}+\frac{2013}{3}+...+\frac{2013}{2012}\right)}{\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}\right)}\)
\(A=\frac{2013\left(\frac{1}{2013}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}\right)}{\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2013}\right)}\)
\(\Rightarrow A=2013\)
Giải thích giùm e dấu bằng thứ nhất và hai được ko ạ?
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a)
\(2^x\left(1+2+2^2+2^3\right)=480\)
\(2^x.15=480\Rightarrow2^x=\frac{480}{15}=32=2^5\Rightarrow x=5\)
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\(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}\right).x=\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+...+\frac{1}{2012}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
tính chỗ có gạch trước nhá
chỗ +...+ là ko biết gì nên tớ cho thành cộng luôn nha
( 2 x 2012 ) : [ 1 : ( 1 + 2 )] + [ 1 : ( 1 + 2 + 3 )] + [ 1 : ( 1 + 2 +....+ 2011 + 2012 )] =
Số các số hạng của dãy 1+..+2012 là : ( 2012 - 1 ) : 1 + 1 = 2012 | 1 + ... + 2012 = ( 2012 + 1 ) x 2012 : 2 = 2025078
4024 : [ 1 : 3 ] + [ 1 : 6 ] + [ 1 : 2025078 ] =
4024 x 3 + 1 + 1 = 1 1 6 2025078
12072 + 1 + 1 = 120721 + 1 = 12072 337514 6 2025078 6 2025078 2025078
==========>NHỚ K MÌNH , CHÚC HỌC GIỎI<===========
Bài làm:
A= 1 + 1/2 + 1/2^3 + 1/2^3 +... + 1/2^2012
1/2.A=1/2 + 1/2^3 + 1/2^3 +... + 1/2^2012+1/2^2013
A-1/2.A=(1 + 1/2 + 1/2^3 + 1/2^3 +... + 1/2^2012)-(1/2 + 1/2^3 + 1/2^3 +... + 1/2^2012+1/2^2013)
1/2.A=1-1/2^2013
A=2-1/2^2012