Tìm giá trị biểu thức:
a) P=\(\dfrac{5}{6}\)+\(\dfrac{5}{12}\)+\(\dfrac{5}{20}\)+\(\dfrac{5}{30}\)+\(\dfrac{5}{42}\)+\(\dfrac{5}{56}\)+\(\dfrac{5}{72}\)+\(\dfrac{5}{90}\)
b) A=\(\dfrac{3}{1.5}\)+\(\dfrac{3}{5.9}\)+\(\dfrac{3}{9.13}\)+...+\(\dfrac{3}{61.65}\). Chứng minh A<13.
Mik đag cần gấppp!!! Thanks!
a)
\(P=\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+\dfrac{5}{30}+\dfrac{5}{42}+\dfrac{5}{56}+\dfrac{5}{72}+\dfrac{5}{90}\\ =\dfrac{5}{2.3}+\dfrac{5}{3.4}+\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{5}{6.7}+\dfrac{5}{7.8}+\dfrac{5}{8.9}+\dfrac{5}{9.10}\\ \Rightarrow\dfrac{1}{5}P=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}\\ =\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\\ =\dfrac{1}{2}-\dfrac{1}{10}=\dfrac{5}{10}-\dfrac{1}{10}\\ =\dfrac{4}{10}=\dfrac{2}{5}\\ \Rightarrow P=\dfrac{2}{5}\cdot5=2\)
