1.Tính tổng: \(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+....+\frac{5}{99.101}\)
2.Rút gọn phân số:
a)\(\frac{2929-101}{2.1919+404}\) b)\(\frac{6.9-2.17}{63.3-119}\)
c)\(\frac{3.13-13.18}{15.40-80}\) d)\(\frac{\left(-5\right)^3.40.4^3}{135.\left(-2\right)^{14}.\left(-100\right)^0}\)
e)\(\frac{-1997.1996+1}{-1995.\left(-1997\right)+1996}\) f)\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}\)
f)\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}\) g)\(\frac{3.7.13.37.39-10101}{505050-70707}\)
h)\(\frac{18.34+\left(-18\right).124}{-36.17+9.\left(-52\right)}\)
Bài 1:
Coi \(A=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+....+\frac{5}{99.101}\)
\(2A=\left(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+....+\frac{5}{99.101}\right).2\)
\(=5.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{99.101}\right)\)
\(=5.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=5.\left(1-\frac{1}{101}\right)\)
\(=5.\frac{100}{101}\)
\(=\frac{500}{101}\Rightarrow A=\frac{500}{101}:2=\frac{250}{101}\)
\(\left(\frac{5}{1}-\frac{5}{3}+\frac{5}{3}-\frac{5}{5}....+\frac{5}{99}-\frac{5}{101}\right):\frac{1}{5}\)
\(\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}.....+\frac{1}{99}-\frac{1}{101}\right).5\)
\(\left(\frac{1}{1}-\frac{1}{101}\right).5\)
\(\frac{100}{101}.5\)
\(\frac{500}{101}\)
2,a,\(\frac{2929-101}{3838+404}\)\(=\frac{2828}{4242}=\frac{2}{3}\)
\(b,\frac{54-34}{189-119}=\frac{20}{70}=\frac{2}{7}\)
\(c,d,e,f,f,g,h\)\(tuong\) \(tu\)
\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...............+\frac{5}{99.101}\)
\(=\frac{5.2}{1.3.2}+\frac{5.2}{3.5.2}+\frac{5.2}{5.7.2}+............+\frac{5.2}{99.101.2}\)
\(=\frac{5}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+.................+\frac{2}{99.101}\right)\)
\(=\frac{5}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.........+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{5}{2}.\left(1-\frac{1}{101}\right)\)
\(=\frac{5}{2}.\frac{100}{101}\)
\(=\frac{250}{101}\)
