Question

 ^{\(2^x-2^y=224\)}

Answer 1

\(2^x-2^y=224\)

\(2^y\left(2^{x-y}-1\right)=2^5.7\)

\(\Rightarrow2^y=2^5\)do đó y = 5

\(\Rightarrow2^{x-y}-1=7\)

do đó \(2^{x-y}=8\)

\(2^{x-y}=2^3\)

\(\Rightarrow x-y=3\)

\(x=5+3\)

\(x=8\)

Answer 2

2^x - 2^y = 224

=> 2^y.(2^x-y - 1) = 214 × 1 = 32 × 7

Do 2^x-y - 1 chia 2 dư 1 => 2^x-y - 1 = 1 hoặc 7

Ta loại trường hợp 2^x-y - 1 = 1 vì khi đó 2^y = 214, vô lí

=> 2^x-y - 1 = 7; 2^y = 32

=> 2^x-y = 7 + 1 = 8 = 2³; 2^y = 2⁵

=> x - y = 3; y = 5

=> y = 5; x = 8

Answer 3

1/1+2  +  1/+1+2+3  +  ...  + 1/1+2+3+...+2014

= 1/(1+2).2:2  +  1/(1+3).3:2  +   ...  + 1/(1 + 2014).2014:2

= 2/2.3  +  2/3.4  +  ...  + 2/2014.2015

= 2.(1/2.3  +  1/3.4  +  ...  + 1/2014.2015)

= 2.(1/2  -  1/3  +  1/3  -  1/4  +  ... + 1/2014  -  1/2015)

= 2.(1/2 - 1/2015)

= 2.1/2 - 2.1/2015

= 1 - 2/2015

= 2013/2015