Question

Giúp mình với !!!

Answer 1

\(1+2+3+...+n=\frac{n\left(n+1\right)}{2}\)

\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+....+\frac{2}{99.100}+\frac{1}{50}=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)+\frac{1}{50}\)

  \(=2\left(\frac{1}{2}-\frac{1}{100}\right)+\frac{1}{50}=1\)