Tính nhanh :
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
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tính nhanh
A=\(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^8}\)
\(=>3A=1+\frac{1}{3}+\frac{1}{3^2}+.....+\frac{1}{3^7}\)
\(=>3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(=>2A=1-\frac{1}{3^8}=>A=\left(1-\frac{1}{3^8}\right):2\)
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Tính nhanh
A= \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+............+\frac{1}{3^8}\)
\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
\(\Rightarrow3A=3\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(\Rightarrow3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(\Rightarrow3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(\Rightarrow2A=1-\frac{1}{3^8}\)
\(\Rightarrow A=\frac{1-\frac{1}{3^8}}{2}\)
\(\Rightarrow A=\frac{3280}{6561}\)
Vậy \(A=\frac{3280}{6561}\)
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\(A=\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\)
\(\Rightarrow3A=1+\frac{1}{3}+...+\frac{1}{3^7}\)
\(\Rightarrow3A-A=\left(1+\frac{1}{3}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^8}\right)\)
\(\Rightarrow2A=1-\frac{1}{3^8}\)
\(\Rightarrow A=\frac{1-\frac{1}{3^8}}{2}\)
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Tính nhanh :
a,1+\(\frac{5}{4}\)+\(\frac{5}{8}\)+\(\frac{5}{16}\)+\(\frac{5}{32}\)+\(\frac{5}{64}\)
b,\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{152}\)
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Tính nhanh
\(\frac{\frac{1}{3}-\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}-\frac{2}{7}-\frac{2}{13}}.\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{64}-\frac{3}{264}}{1-\frac{1}{4}-\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)
Bài 1:Tính nhanh:
a,\(\frac{2}{3}+\frac{4}{6}+\frac{6}{3}\)
b,\(\frac{3}{4}+\frac{6}{8}+\frac{18}{12}\)
Bài 2:Tính:
a,\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
b,\(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}\)
a, \(\frac{2}{3}+\frac{2}{3}+\frac{6}{3}=\frac{10}{3}\)
b,\(\frac{3}{4}+\frac{3}{4}+\frac{3}{2}=\frac{6}{4}+\frac{3}{2}=\frac{3}{2}+\frac{3}{2}=\frac{6}{2}=3\)
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1/tính nhanh
a/\(A=\frac{7}{8}:\left(\frac{2}{9}-\frac{1}{18}\right)+\frac{7}{8}:\left(\frac{1}{36}-\frac{5}{12}\right)\)
b/\(B=\frac{1+0,6-\frac{3}{7}}{\frac{8}{3}+\frac{8}{5}-\frac{8}{7}}-\frac{\frac{1}{3}+0,25-\frac{1}{5}+0,125}{\frac{7}{6}+\frac{7}{8}-0,7+\frac{7}{16}}\)
A= 7/8:(4/18-1/18)+7/8:(1/36-15/36)
=7/8:1/6+7/8:(-7/18)
=7/8:(1/6+-7/18)=7/8:(3/18+-7/18)=7/8:(-2/9)=-63/18=-7/2
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TÍNH NHANH:
A=\(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
B=\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{100.101}\)
a) \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
\(\Rightarrow3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(\Rightarrow3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)(áp dụng quy tắc dấu ngoặt )
\(3A-A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}-\frac{1}{3}-\frac{1}{3^2}-\frac{1}{3^3}-...-\frac{1}{3^8}\)
\(3A-A=1+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{3^2}-\frac{1}{3^2}\right)+...+\left(\frac{1}{3^7}-\frac{1}{3^7}\right)-\frac{1}{3^8}\)
\(\Rightarrow2A=1+0+0...+0-\frac{1}{3^8}\)
\(2A=1-\frac{1}{3^8}\)
\(2A=\frac{3^8-1}{3^8}\)
\(A=\frac{3^8-1}{3^8}\div2=\frac{3^8-1}{3^8}.\frac{1}{2}=\frac{3^8-1}{3^8.2}\)
b) \(B=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{100.101}\)
\(\Rightarrow B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\)(áp dụng quy tắc dấu ngoặt )
\(B=\frac{1}{1}-\left(\frac{1}{2}-\frac{1}{2}\right)-\left(\frac{1}{3}-\frac{1}{3}\right)-...-\left(\frac{1}{100}-\frac{1}{100}\right)-\frac{1}{101}\)
\(B=\frac{1}{1}-0-0-0...-0-\frac{1}{101}\)
\(B=\frac{1}{1}-\frac{1}{101}\)
\(B=\frac{100}{101}\)
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Tính nhanh (nếu có thể):
a, \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^8}\)
b, \(\frac{-1}{100.99}+\frac{-1}{99.98}+\frac{-1}{98.97}+..........+\frac{-1}{3.2}+\frac{-1}{2.1}\)
b) \(GọiB=\frac{-1}{100.99}+\frac{-1}{99.98}+...+\frac{-1}{2.1}\)
\(2B=\frac{-2}{100.99}+\frac{-2}{99.98}+...+\frac{-2}{2.1}\)
\(2B=\frac{-1}{100}-\frac{-1}{99}+\frac{-1}{99}-\frac{-1}{98}+...+\frac{-1}{2}-\frac{-1}{1}\)
\(2B=\frac{-1}{100}-\frac{-1}{1}\)
\(2B=\frac{99}{100}\Rightarrow B=\frac{99}{100}:2=\frac{99}{200}\)
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Đặt \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
\(< =>3A=\frac{3}{3}+\frac{3}{3^2}+\frac{3}{3^3}+...+\frac{3}{3^8}\)
\(< =>3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(< =>3A-A=1-\frac{1}{3^8}=\frac{3^8-1}{3^8}\)
\(< =>A=\frac{3^8-1}{\frac{3^8}{2}}\)
Bài 1 : tính nhanh
a) \(A=\frac{1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}}:\frac{3+\frac{3}{2}+\frac{3}{3}+\frac{3}{4}}{2-\frac{2}{2}+\frac{2}{3}-\frac{2}{4}}\)
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