Đặt   \(A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^n}\)

=> \(2A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{n-1}}\)

=> \(2A-A=\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{n-1}}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^n}\right)\)

=> \(A=\frac{1}{2}-\frac{1}{2^n}\) 

=> \(A=\frac{2^n}{2^n.2}-\frac{2}{2^n.2}=\frac{2^n-2}{2^n.2}=\frac{2^n+\left(-2\right)}{2^n+2^n}\)

Vì  -2 < 2ⁿ => \(2^n+\left(-2\right)<2^n+2^n\)  =>  \(\frac{2^n+\left(-2\right)}{2^n+2^n}<1\)  =>  \(A<1\)       

=> \(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^n}<1\)   (đpcm)

1 By the end of December, John (work) will have worked as a reporter for ten years.

2 By the time you arrive, I (finish) will have finished writing an easay.

3 I (give) will give him your message when I (see) see him.

4 He certainly (not do) will not have done all his homework by ten tonight.

5 Don't call him at 2:30 p.m. He (interview) will be interviewing job applicants at that time.

6 The teacher hopes we (pass) will pass our exams.

7 By this time next week, he (write) will have writen his novel for 6 months.

8 They (arrive) will arrive on Wednesday.

9 I hope the weather (be) will be fine tonight.

10 Will You (finish) have finished your homework by 9 tonight ?

nhảy xuống chết luôn .

Có trứng mới nở ra gà được

Lịch sử dài nhất

 23x +53y=109 
<=> x = (109 - 53y)/23 = 4 - 2y +(17-7y)/23 
x nguyên nên 17-7y= 23m => y = (17-23m)/7 = 2 -3m +(3 - 2m)/7 
y nguyên nên: 3 - 2m = 7n => m = (3-7n)/2 = 1 - 3n +(1 -n)/2 
m nguyên nên: 1 -n = 2p => n = 1-2p 
(m,n,p là số nguyên) 
Từ n = 1-2p => m = 1 - 3(1-2p) + p = -2 +7p 
=> y = 2 -3(-2+7p) + 1- 2p = 9 -23p 
=> x = 4 - 2(9 -23p) -2 +7p = 2 -18 +46p +7p = 53p - 16. 
Vậy x = 53p - 16; y = 9 - 23p 

mk mới học lớp 5 thui ! sorry nhưng mk sẽ bảo anh trai mk giúp bạn nhé !

Số nhỏ nhất có 4 chữ số là:1000.

Vậy 1/5 của 1000 là :1000x1/5=200

Hiếu Trần Quốc giải sai rồi!