Question

[dinhkhachoang]

tinh nhanh

1/2+1/2^2+1/2^3+...........+1/2^10

Answer 1

[Đinh Đức Hùng]

Đặt A = \(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)

Nhân cả hai với 2 ta được :

2A = \(2\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)

=> 2A = \(1+\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

Trừ 2A cho A , ta được :

2A - A = \(\left(1+\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)-\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)

=> A = \(1-\frac{1}{2^{10}}\)

Answer 2

[dinhkhachoang]

A=1/2+1/2^2+1/2^3+.............+1/2^10

2A=1+1/2+1/2^2+.............+1/2^9

2a-a=(1/2+1/2^2+1/2^3.....+1/2^10)-(1+1/2+1/2^2............+1/2^9)

=>a=1-1/2^10

=>a=1-1/1024

=>A=1023/1024