Question

1/3+1/6+1/12+1/24+1/48+1/96

Answer 1

Đặt tổng các phân số trên là A ta có

\(\frac{A}{2}=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)

\(\frac{A}{2}=A-\frac{A}{2}=\frac{1}{3}-\frac{1}{192}=\frac{63}{192}\Rightarrow A=\frac{2x63}{192}=\frac{126}{192}=\frac{21}{32}\)
 

Answer 2

1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96

= 1x32/2x32 + 1x16/6x16 + 1x8/12x8 + 1x4/24x4 + 1x2/48x2 + 1/96

= 32/96 + 16/96 + 8/96 + 4/96 + 2/96 + 1/96

= 63/96