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8 tháng 1 2017

a)

\(2^x\left(1+2+2^2+2^3\right)=480\)

\(2^x.15=480\Rightarrow2^x=\frac{480}{15}=32=2^5\Rightarrow x=5\)

15 tháng 1 2017

Chính Xác 100% là X=5 

k cho mink nhé các pạn

8 tháng 1 2017

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\)

\(\Rightarrow2^x\cdot1+2^x\cdot2^1+2^x\cdot2^2+2^x\cdot2^3=480\)

\(\Rightarrow2^x\left(1+2^1+2^2+2^3\right)=480\)

\(\Rightarrow2^x\cdot15=480\)

\(\Rightarrow2^x=32\Rightarrow2^x=2^5\Rightarrow x=5\)

8 tháng 1 2017

b) \(\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right)x=\frac{2012}{1}+\frac{2011}{2}+...+\frac{2}{2011}+\frac{1}{2012}\)

\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right)x=\left(\frac{2011}{2}+1\right)+...+\left(\frac{2}{2011}+1\right)+\left(\frac{1}{2012}+1\right)+1\)

\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right)x=\frac{2013}{2}+...+\frac{2013}{2011}+\frac{2013}{2012}+\frac{2013}{2013}\)

\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}\right)x=2013\left(\frac{1}{2}+...+\frac{1}{2012}+\frac{1}{2013}\right)\)

\(\Rightarrow x=2013.\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}+\frac{1}{2013}}\)

\(\Rightarrow x=2013\)

Vậy \(x=2013\)

26 tháng 7 2015

Ta có: \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2010^2}

22 tháng 4 2015

Tử số = T = \(\frac{2012}{1}+\frac{2011}{2}+\frac{2010}{3}+.....+\frac{1}{2012}\)\(=\left(\frac{2012}{1}+1\right)+\left(\frac{2011}{2}+1\right)+\left(\frac{2010}{3}+1\right)+...+\left(\frac{1}{2012}+1\right)-2012\)\(=2013+\frac{2013}{2}+\frac{2013}{3}+...+\frac{2013}{2012}-2012\)

\(=\frac{2013}{2}+\frac{2013}{3}+...+\frac{2013}{2012}+1\)

\(=\frac{2013}{2}+\frac{2013}{3}+....+\frac{2013}{2012}+\frac{2013}{2013}\)

\(=2013\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2012}+\frac{1}{2013}\right)\)

Dặt mẫu số là M thì y = \(\frac{2013.M}{M}\)= 2013

5 tháng 7 2017

a) \(\frac{2^{10}+1}{2^{10}-1}\)và \(\frac{2^{10}-1}{2^{10}-3}\)

Ta có chính chất phân số trung gian là \(\frac{2^{10}+1}{2^{10}-3}\)

\(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}\) ; \(\frac{2^{10}-1}{2^{10}-3}< \frac{2^{10}+1}{2^{10}-3}\)

Vì \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}+1}{2^{10}-3}>\frac{2^{10}-1}{2^{10}-3}\)

Nên \(\frac{2^{10}+1}{2^{10}-1}>\frac{2^{10}-1}{2^{10}-3}\)

b) \(A=\frac{2011}{2012}+\frac{2012}{2013}\)và \(B=\frac{2011+2012}{2012+2013}\)

Ta có : \(A=\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2013}+\frac{2012}{2013}=\frac{2011+2012}{2013}>\frac{2011+2012}{2012+2013}=B\)

Vậy A > B 

Có gì  sai cho sorry

a,

\(\frac{2^{10}+1}{2^{10}-1}=1+\frac{2}{2^{10}-1}< 1+\frac{2}{2^{10}-3}=\frac{2^{10}-1}{2^{10}-3}\)

b,

\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}=\frac{2011+2012}{2012+2013}\)