Question

[Vũ Anh Khôi]

tính tổng các số sau a) 1+1/2+1/4+1/8+1/16

Answer 1

[boi đz]

Gọi \(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}\) là A

\(A=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}\)

\(2\times A=2+1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}\)

\(2\times A-A=\left(2+1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}\right)\)

\(A=2+\left(1-1\right)+\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+\left(\dfrac{1}{8}-\dfrac{1}{8}\right)-\dfrac{1}{16}\)

\(A=2+0+0+0+0-\dfrac{1}{16}\)

\(A=2-\dfrac{1}{16}\)

\(A=\dfrac{32}{16}-\dfrac{1}{16}\)

\(A=\dfrac{31}{16}\)