nani?

Xét bài toán : 

So sánh \(\frac{a}{b}\)và \(\frac{a+m}{b+m}\)( a>b , m>0)

Có \(\frac{a}{b}=\frac{a\left(b+m\right)}{b\left(b+m\right)}=\frac{ab+am}{b\left(b+m\right)}\)

   \(\frac{a+m}{b+m}=\frac{b\left(a+m\right)}{b\left(b+m\right)}=\frac{ab+bm}{b\left(b+m\right)}\)

Mà a>b => am > bm => \(\frac{ab+am}{b\left(b+m\right)}>\frac{ab+bm}{b\left(b+m\right)}\)hay \(\frac{a}{b}>\frac{a+m}{b+m}\)

Áp dụng : \(A=\frac{3^{2017}+5}{3^{2015}+5}>\frac{3^{2017}+5+4}{3^{2015}+5+4}=\frac{3^{2017}+9}{3^{2015}+9}=\frac{3^2\left(3^{2017}+9\right)}{3^2\left(3^{2015}+9\right)}\)

                     \(=\frac{3^{2015}+1}{3^{2013}+1}=B\)

=> A > B

\(A=1+5^2+5^3+...+5^{2015}+5^{2016}\)

\(5A=5+5^3+5^4+...+5^{2016}+5^{2017}\)

\(4A=\left(5+5^3+5^4+...+5^{2016}+5^{2017}\right)-\left(1+5^2+5^3+...+5^{2015}+5^{2016}\right)\)

\(=5+5^{2017}-\left(1+5^2\right)\)

\(=4+5^{2017}-5^2\)

\(A=\frac{4+5^{2017}-5^2}{4}\)

Ta có : 5A = 5 + 5^3 + 5^4 + ... + 5^2016 + 5^2017

  =>    5A - A = ( 5 + 5^3 + 5^4 + ... + 5^2016 + 5^2017 ) - ( 1 + 5^2 + 5^3 + ... + 5^2015 + 5^2016 )

  =>         4A = 4 + 5^2 + 5^2017

  =>           A = ( 4 + 5^2 + 5^2017 )/4

các bạn khác kq của mik

5^2017-1/4

\(\left(x+\dfrac{1}{3}\right)\times\dfrac{9}{14}\times\dfrac{7}{3}-\dfrac{1}{3}=1:\dfrac{9}{5}\\ \Rightarrow\left(x+\dfrac{1}{3}\right)\times\dfrac{3}{2}-\dfrac{1}{3}=\dfrac{5}{9}\\ \Rightarrow\left(x+\dfrac{1}{3}\right)\times\dfrac{3}{2}=\dfrac{5}{9}+\dfrac{1}{3}\\ \Rightarrow\left(x+\dfrac{1}{3}\right)\times\dfrac{3}{2}=\dfrac{8}{9}\\ \Rightarrow x+\dfrac{1}{3}=\dfrac{8}{9}:\dfrac{3}{2}\\ \Rightarrow x+\dfrac{1}{3}=\dfrac{16}{27}\\ \Rightarrow x=\dfrac{16}{27}-\dfrac{1}{3}\\ \Rightarrow x=\dfrac{7}{27}\)

a) \(\left(x-\frac{1}{2}\right)^4=\frac{1}{81}\)

\(\Rightarrow\left(x-\frac{1}{2}\right)^4=\left(\frac{1}{3}\right)^4\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{2}=\frac{1}{3}\\x-\frac{1}{2}=\frac{-1}{3}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{5}{6}\\x=\frac{1}{6}\end{cases}}\)

Vậy ...

trả lời

\(x=\frac{1}{6}\)

hk tốt

b) ta có: \(5^{50}=\left(5^2\right)^{25}=25^{25}\); \(3^{75}=\left(3^3\right)^{25}=27^{25}\).

Mà \(25^{25}< 27^{25}\)nên \(5^{50}< 3^{75}\)

Gọi tử số của \(S\)là :\(A=1+2+2^2+2^3+...+2^{2015}\)

\(2A=2+2^2+2^3+...+2^{2016}\)

\(2A-A=\left(2+2^2+2^3+...2^{2016}\right)-\left(1+2+2^2+...+2^{2015}\right)\)

\(A=1-2^{2016}\)

\(\Rightarrow S=\frac{1-2^{2016}}{1-2^{2016}}=1\)