Question

giải giúp mình với!!!

cách giải lun nha!!!

Answer 1

\(P=\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+...+\dfrac{1}{1+2+3+...+50}\)

\(\Rightarrow P=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{1275}\)

\(\Rightarrow\dfrac{1}{2}P=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{2550}\)

\(\Rightarrow\dfrac{1}{2}P=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{50.51}\)

\(\Rightarrow\dfrac{1}{2}P=\dfrac{1}{2}-\dfrac{1}{51}=\dfrac{49}{102}\)

\(\Rightarrow P=\dfrac{49}{51}\)