Ta có : 

\(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\)

\(2A=1+2+\frac{1}{2}+...+\frac{1}{2^{2011}}\)

\(2A-A=\left(1+2+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)

\(A=2-\frac{1}{2^{2012}}\)

\(A=\frac{2^{2013}-1}{2^{2012}}\)

Vậy \(A=\frac{2^{2013}-1}{2^{2012}}\)

\(A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\)

=>2A=\(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\)

=>2A-A=\(\left(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)=2-\frac{1}{2^{2012}}\)

=>A=\(\frac{2^{2013}-1}{2^{2012}}\)

ta có :

2.A=1/2+2/2²+...+1/2²⁰¹³

2.A-A=(2+1+1/2²+...+1/2²⁰¹¹)-(1+1/2+1/2²+...+1/2²⁰¹²)

=>A= 2-1/2²⁰¹²

2A=2+1+1/2+1/2^2+...+1/2^2011

2A-A=A=(2+1+1/2+1/2^2+...+1/2^2011)-(1+1/2+1/2^2+...+1/2^2012)

A=2-1/2^2012

a.Chứng tỏ rằng B = 1/2² + 1/3² + 1/4² + 1/5² + 1/6² + 1/7² +1/8² < 1

b.Cho S = 3/1.4 + 3/4.7 + 3/7.10 +......+3/40.43 + 3/43.46 hãy chứng tỏ rằng S < 1

Xin lỗi mọi người mình tính đặt câu hỏi nhưng ấn nhầm phần trả lời ạ!

A=(ghi lại biieur thức)

2A=2+1+1/2+1/2^2+….+1/2^2011

2A-A=A=(2+1+1/2+1/2^2+….+1/2^2011)-(1+1/2+1/2^2+...+1/2^2012)

A=2-1/2^2012

1/2 A= 1/2+1/2^2+1/2^3+1/2^4+...........+1/2^2013

=>A-1/2A= 1 -1/2^2013

=>1/2A=1 -1/2^2013

=>A=(1 - 1/2^2013) : 1/2

2A = 2 + 1 + 1/2 + 1/2² + 1/2³ + ... + 1/2²⁰¹¹

mà A = 1 + 1/2 + 1/2² + 1/2³ + ... + 1/2²⁰¹²

2A - A = 2 - 1/2²⁰¹²

A = 2 - 1/2²⁰¹²

Ta có A=1+1/2+1/2^2+1/2^3+........+1/2^2012

=>2A=2+1+1/2+1/2^2+.......+1/2^2011

=>2A-A=(2+1+1/2+1/2^2+.....+1/2^2011)-(1+1/2+1+1/2^2+1/2^3+.....+1/2^2012)

=>A=\(2-\frac{1}{2^{2012}}\)

\(A=\frac{2^{2013-1}}{2^{2012}}\)

A=đã cho.

1/2*A=1/2+1/2^2+1/2^3+...+1/2^2012+1/2^2013.

A-1/2*A=1-1/2^2013(khử).

1/2*A=1-1/2^2013.

A=2*(1-1/2^2013).

A=2-2/2^2013.

A=2-1/2^2012.

2A=2+1+1/2+1/2^2+1/2^3+...+1/2^2011
2A-A=(2+1+1/2+1/2^2+1/2^3+...+1/2^2011)-(1+1/2+1/2^2+1/2^3+...+1/2^2012)
A=2-2/2012
k cho mik nhé

1+1/2012