A = 1/2 - 1/2^2 + 1/2^3 - 1/2^4 + ... + 1/2^2017

2A = 1 - 1/2 + 1/2^2 - 1/2^3 + .... + 1/2^2016

2A + A = 1 + 1/2^2017

=> A = (1 + 1/2^2017) : 3 

Đặt \(A=1+3+3^2+3^3+...+3^{2016}\)

\(\Rightarrow3A=3+3^2+3^3+3^4...+3^{2017}\)

\(\Rightarrow3A-A=3+3^2+3^3+3^4...+3^{2017}-1-3-3^2-3^3-3^{2016}\)

\(\Rightarrow2A=3^{2017}-1\)

\(\Rightarrow A=\frac{1}{2}\left(3^{2017}-1\right)\)

\(\Rightarrow A=\frac{-1}{2}\left(1-3^{2017}\right)\)

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

Đặt A = 1 + 3 + 3^2 + 3^3 + ... +  3^2016

=> 3A = 3 +  3^2 + 3^3 + 3^4 + ... + 3^2017

=> 3A - A = 3^2017 - 1

=> 2A = 3^2017 - 1

=> A = (3^2017 - 1) : 2

\(25\%x+x=\frac{5}{2}\)

\(\frac{1}{4}x+1x=\frac{5}{2}\)

\(\left(\frac{1}{4}+1\right)x=\frac{5}{2}\)

\(\frac{5}{4}x=\frac{5}{2}\)

\(x=\frac{5}{2}:\frac{5}{4}\)

\(x=2\)

Thank you bạn nhé

\(\left|x+1\right|=3\)

\(\Rightarrow\orbr{\begin{cases}x+1=3\\x+1=-3\end{cases}\Rightarrow\orbr{\begin{cases}x=3-1\\x=\left(-3\right)-1\end{cases}\Rightarrow}\orbr{\begin{cases}x=2\\x=-4\end{cases}}}\)

Vậy .............

| x + 1 | = 3

=> x + 1 = 3 hoặc x + 1 = -3

* x+1=3

x=3-1

x=2

*x+1=-3

x=-3-1

x=-4

Vậy x=2 ; x=-4

\(2^x+1=25\)

\(2^x=25-1\)

\(2^x=24\)

Tớ chi giải đến đây đc thôi vì luy thừa cũa 2 ko có 24

\(2^x+1=25\)

\(\Rightarrow2^x=25-1\)

\(\Rightarrow2^x=24\)

\(\Rightarrow x\in\varnothing\)

1) How about your favourite weather?

2)Tran Phu Street is longer than Le Loi street

3)Ha Noi capital is smaller than HCM city

How about your favourite weather
Tran phu street isn't  as short as Le loi street

Hà noi capital isn't as big as HCM city

Đặt A =\(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\)

2A = \(2\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\right)\)

2A = \(2+1+\frac{1}{2}+...+\frac{1}{2^{99}}\)

2A - A = \(\left(2+1+\frac{1}{2}+...+\frac{1}{2^{99}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\right)\)

A = \(2-\frac{1}{2^{100}}\)

Đặt \(C=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\)

\(\Rightarrow2C=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{101}}\)

\(\Rightarrow2C-C=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{101}}-1-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{100}}\)

\(\Rightarrow2C-C=2+\frac{1}{2^{101}}\)

a) cuốn sách đó có số trang là :

\(40:\frac{1}{5}=200\left(trang\right)\)

ngày 2 đọc số trang là :

\(\left(200-40\right)\cdot\frac{1}{4}=40\left(trang\right)\)

ngày 3 đọc số trang là :

\(200-40-40=120\left(trang\right)\)

b) tỉ số phần trăm giữa ngày 1 và ngày 3 là :

\(\frac{40}{120}\%=0,33...\%\)

Đáp số : ...

\(\left(B\right)33,33...\%\)

Xét: \(\left(a+b+c\right)\left(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}\right)=7\cdot\frac{7}{10}=\frac{49}{10}\)

\(\Leftrightarrow\frac{a+b}{a+b}+\frac{c}{a+b}+\frac{a+c}{a+c}+\frac{b}{a+c}+\frac{b+c}{b+c}+\frac{a}{b+c}=\frac{49}{10}\)

\(\Rightarrow3+\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=\frac{49}{10}\Rightarrow A=\frac{19}{10}\)

Vì \(19=19\) và \(\frac{1}{11}< \frac{1}{10}\Rightarrow\frac{19}{11}< \frac{19}{10}\Rightarrow S>\frac{19}{11}\)

tại sao lại là 7/10 vậy ?

Sơ đồ đây nhé :