tinh nhanh
1/3+1/6+1/12+1/24+1/48+1/96
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\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)
\(\Rightarrow3A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(\Rightarrow3A=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}\)
\(\Rightarrow3A=1+1-\frac{1}{32}\)
\(\Rightarrow3A=2-\frac{1}{32}\)
\(\Rightarrow A=\left(2-\frac{1}{32}\right):3=\frac{21}{32}\)
P/s : Đúng nha
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}=\frac{21}{32}\)
Nhớ click cho mik nha !!!!!!!!!!!!!!!!!!!!!
1/3 + 1/6+1/12+1/24+1/48+1/96
= 2/3 – 1/3 + 1/3 – 1/6+1/6- 1/12+1/12- 1/24+1/24-
1/48+1/48-1/96
=2/3_1/96
= 63/96
= 21/32
= 1-1/3+1/3-1/6+1/6-1/12+1/12-1/24+1/24-1/48+1/48-1/96+1/96-1/192
= 1-1/192 = 191 / 192
Đặt tổng các phân số trên là A ta có
\(\frac{A}{2}=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)
\(\frac{A}{2}=A-\frac{A}{2}=\frac{1}{3}-\frac{1}{192}=\frac{63}{192}\Rightarrow A=\frac{2x63}{192}=\frac{126}{192}=\frac{21}{32}\)
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
1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192 + 1/384 = 85/128
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)
\(=\frac{1}{2}+\frac{1}{8}+\frac{1}{32}\)
\(=\frac{5}{8}+\frac{1}{32}\)
\(=\frac{21}{32}\)
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