Question

1-1/2 + 2 - 2/3²- 1/2³ -……….-1/2¹⁰

Answer 1

Sửa đề:

\(A=1-\dfrac{1}{2}-\dfrac{1}{2^2}-....-\dfrac{1}{2^{10}}\)

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

Đặt:

\(B=\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{10}}\)

\(2B=2\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{10}}\right)\)

\(2B=1+\dfrac{1}{2}+....+\dfrac{1}{2^9}\)

\(2B-B=\left(1+\dfrac{1}{2}+...+\dfrac{1}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{10}}\right)\)

\(B=1-\dfrac{1}{2^{10}}\)

Thay vào A

\(A=1-\left(1-\dfrac{1}{2^{10}}\right)\)

\(A=\dfrac{1}{2^{10}}=\dfrac{1}{1024}\)