Question

a=1/2 +1/4+1/8+.....+1/512+1/1024

Answer 1

A = 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + ..... + 1/256 - 1/512 + 1/512 - 1/1024

A = 1 - 1/1024

A = 1023/1024

Answer 2

\(A=\frac{1023}{1024}\)

Answer 3

A = \(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ .....+\(\frac{1}{512}\)+\(\frac{1}{1024}\)

Gấp biểu thức A lên 2 lần ta có :

A x 2 = (\(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ .....+ \(\frac{1}{512}\)+ \(\frac{1}{1024}\)) x 2

A x 2 = \(\frac{1x2}{2}\)+ \(\frac{1x2}{4}\)+ \(\frac{1x2}{8}\)+.....+ \(\frac{1x2}{512}\)+ \(\frac{1x2}{1024}\)

A x 2 = \(1\)+ \(\frac{1}{2}\)+\(\frac{1}{4}\)+....+\(\frac{1}{256}\)+\(\frac{1}{512}\)

A x (2 - 1)= 1 + \(\frac{1}{2}\)+\(\frac{1}{4}\)+ ....+ \(\frac{1}{256}\)+ \(\frac{1}{512}\)-  \(\frac{1}{2}\)-\(\frac{1}{4}\)-\(\frac{1}{8}\)-......- \(\frac{1}{512}\)-\(\frac{1}{1024}\)

A = \(1\)- \(\frac{1}{1024}\)

A = \(\frac{1024}{1024}\)- \(\frac{1}{1024}\)

A = \(\frac{1023}{1024}\)