sai đề rồi bn ơi A=A+2^2+2^3+2^4+...+2^20= ko ra kq nka 

nếu đúng thì k , chúc bn hc tốt

\(Ta\)có : 

\(\frac{1}{2^2}< \frac{1}{1.2};\frac{1}{3^2}< \frac{1}{2.3};...;\frac{1}{20^2}< \frac{1}{19.20}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{20^2}< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{19.20}\)

\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{19}-\frac{1}{20}\)

\(\Rightarrow A< 1-\frac{1}{20}< 1\left(Đpcm\right)\)

Chúc bạn học tốt !!! 

A=4+2² +2³ +2⁴ +....2²⁰

A=2²+2² +2³ +2⁴ +....2²⁰

2A=2(4+2² +2³ +2⁴ +....2²⁰)

2A=2³+2³ +2⁴ +2⁵ +....2²¹

2A-A=(2³+2³ +2⁴ +2⁵ +....2²¹)-(2²+2² +2³ +2⁴ +....2²⁰)

A=2³+2²¹-(2²+2²)

A=8+2²¹-8

A=2²¹=2097152

S=1/2+1/2²+1/2³+....+1/2²⁰<1

2S=1+1/2+1/2²+1/2³+....+1/2

2S=1+S-1/2²⁰

2S-S=1-1/2²⁰

S=1-1/2²⁰

1-1/2²⁰<1

=> S<1

Hơi khó hiểu chút nha bn

bn chi can ghep 4 vs 4^2; 4^3 vs 4^4 cu tuong tu nhu the

bn se ra cap dau tien thi bang 20, cap thu 2 thi ban 4^2.(4+4^2)=4^2.20

tuong tu nhu the rut thua so chung 20 ra,20=4.5

suy ra A chia het cho 5

Chuc ban hoc tot, k minh nha

có: 1/3^2<1/2.3; 1/4^2<1/3.4:...: 1/100^2<1/99.100

Mà: 1/1.2+1/2.3+...+1/99.100=1-1/2+1/2-1/3+...+1/99-1/100

=1-1/100

=99/100

=> 1/3^2+1/4^2+...+1/100^2<99/100<1

=> đpcm

UNDERSTAND ???

đặt A= biểu thức trên

tao có 

A<1/2.3+1/3.4+...+1/99.100

A<1/2-1/3+1/3-1/4+...+1/99-1/100

A<1/2-1/100<1/2

SUY RA A<1/2(DPCM)