\(A=\dfrac{5}{1.3}+\dfrac{5}{3.5}+\dfrac{5}{5.7}+...+\dfrac{5}{99.101}\)
\(A=5.\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{99.101}\right)\)
\(A=5.\dfrac{1}{2}.\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\right)\)
\(A=\dfrac{5}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
\(A=\dfrac{5}{2}.\left(1-\dfrac{1}{101}\right)\)
\(A=\dfrac{5}{2}.\dfrac{100}{101}=\dfrac{5.50}{101}=\dfrac{250}{101}=2\dfrac{48}{101}\)
A = \(\dfrac{5}{1.3}+\dfrac{5}{3.5}+\dfrac{5}{5.7}+...+\dfrac{5}{99.101}\)
= \(\dfrac{5}{2}.\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\right)\)
= \(\dfrac{5}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
= \(\dfrac{5}{2}.\left(1-\dfrac{1}{101}\right)\)
= \(\dfrac{5}{2}.\dfrac{100}{101}\)
= \(\dfrac{250}{101}\)
A=5(1/1*3 + 1/3*5 + 1/5*7 +...+ 1/99*101)
A=5.1/2(2/1*3 + 2/3*5 + 2/5*7 +...+ 2/99*101)
A=5.1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/100)
A=5.1/2(1-1/100)
A=5.1/2.99/100
A=5/2.99/100
A=99/40
