\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^8}\)
\(=>3A=1+\frac{1}{3}+\frac{1}{3^2}+.....+\frac{1}{3^7}\)
\(=>3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(=>2A=1-\frac{1}{3^8}=>A=\left(1-\frac{1}{3^8}\right):2\)
tính nhanh :
a) \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)\)
b) \(2.\frac{3}{7}+\left(\frac{2}{9}-1\frac{3}{7}\right)-\frac{5}{3}:\frac{1}{9}\)
c) \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}\)
d) \(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right).\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)
Tính :
a ) \(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right)...\left(\frac{1}{99}+1\right)\)
b )\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right)...\left(\frac{1}{100}-1\right)\)
c ) \(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)
Tính :
\(A=\frac{3}{1}+\frac{3}{1+2}+\frac{3}{1+2+3}+\frac{3}{1+2+3+4}+...+\frac{3}{1+2+3+4+....+100}\)
1) Tính:
a) \(\frac{\frac{1}{9}-\frac{5}{6}-4}{\frac{7}{12}-\frac{1}{36}-10}\)
b) \(\frac{\frac{15}{8}-\frac{15}{6}-\frac{15}{32}+\frac{15}{64}}{3-\frac{3}{2}-\frac{3}{4}+\frac{3}{8}}\)
Tính :
\(\left(\frac{3}{5}-\frac{1}{2}+\frac{7}{3}\right)-\left(\frac{1}{3}-\frac{5}{2}+\frac{1}{5}\right)-\left(-\frac{3}{5}+3-\frac{5}{3}\right)\)
Bài 14 : Tìm x biết :
e) \(\frac{-2}{3}-\frac{1}{3}\left(2x-5\right)=\frac{3}{2}\) g) \(\frac{2}{5}x+\frac{1}{2}=\frac{-3}{4}\) h) \(\frac{1}{3}x-8=\frac{1}{2}\) i) \(x-\frac{1}{4}=\frac{5}{8}.\frac{2}{3}\)
Tính nhanh
a) \(\frac{6}{7}:\left(\frac{1}{2}\text{X}\frac{3}{4}\right)-\frac{5}{8}\)
b) 34-2:\(\left(\frac{3}{5}-\frac{1}{2}\right)\)
c) \(\left(4\frac{1}{2}+\frac{1}{2}:5\frac{1}{2}\right)\text{X}\left(3\frac{5}{6}+2\frac{1}{6}\text{x}6\right)\)
1) Tính :
a) A = ( \(1-\frac{1}{2}\) ) + ( \(1-\frac{1}{4}\) ) + ( \(1-\frac{1}{8}\) ) + .......+ ( \(1-\frac{1}{512}\) ) + ( \(1-\frac{1}{1024}\) )
b) B = ( \(\frac{5^3}{6}+\frac{5^3}{12}+\frac{5^3}{20}+\frac{5^3}{42}+\frac{5^3}{56}+\frac{5^3}{72}+\frac{5^3}{90}\) ) : \(\frac{1124.2247-1123}{1124+1123.2247}\)
c) C = \(\frac{1}{3}+\frac{1}{9}+\frac{1}{18}+\frac{1}{30}+......+\frac{1}{14850}\)
Tính:
a) A = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\)
b) \(B=3+\frac{3}{1+2}+\frac{3}{1+2+3}+...+\frac{3}{1+2+...+100}\)
