\(A=\dfrac{5}{3.5}+\dfrac{5}{5.7}+\dfrac{5}{7.9}+...+\dfrac{5}{97.99}\)
\(A=\dfrac{5}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{97.99}\right)\)
Nhận xét:
\(\dfrac{2}{3.5}=\dfrac{1}{3}-\dfrac{1}{5};\dfrac{2}{5.7}=\dfrac{1}{5}-\dfrac{1}{7};...;\dfrac{2}{97.99}=\dfrac{1}{97}-\dfrac{1}{99}\)
\(\Rightarrow A=\dfrac{5}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(\Rightarrow A=\dfrac{5}{2}\left(\dfrac{1}{3}-\dfrac{1}{99}\right)\)
\(\Rightarrow A=\dfrac{5}{2}.\dfrac{32}{99}=\dfrac{80}{99}\)
Vậy A=\(\dfrac{80}{99}\)
A= 5/2. (2/3.5+2/5.7+2/7.9+...+/97.99) A= 5/2. ( 1/3-1/5+1/5-1/7+1/7-1/9+...+/97+1/99) A= 5/2. ( 1/3-1/99) A= 5/2.32/99 A=80/99 B=5/2. (2/1.3+2/3.5+2/5.7+...+2/59.61) B= 5/2. (1-1/3+1/3-1/5+1/5-1/7+...+1/59-1/61) B= 5/2. (1- 1/61) B = 5/2. 60/61 B = 300/122=150/61
\(B=\dfrac{5}{1.3}+\dfrac{5}{3.5}+\dfrac{5}{5.7}+...+\dfrac{5}{59.61}\)
\(B=\dfrac{5}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{59.61}\right)\)
Nhận xét :
\(\dfrac{2}{1.3}=1-\dfrac{1}{3};\dfrac{2}{3.5}=\dfrac{1}{3}-\dfrac{1}{5};\dfrac{2}{5.7}=\dfrac{1}{5}-\dfrac{1}{7};...;\)
\(\dfrac{2}{59.61}=\dfrac{1}{59}-\dfrac{1}{61}\)
\(\Rightarrow B=\dfrac{5}{2}\left(1-\dfrac{1}{61}\right)\)
\(\Rightarrow B=\dfrac{5}{2}.\dfrac{60}{61}=\dfrac{150}{61}\)
Vậy B=\(\dfrac{150}{61}\)
