Question

Cmr   7/12 < A< 5/6

Biết A=1-1/2+1/3-1/4+...+1/47-1/48+1/49-1/50

Answer 1

\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{47}-\frac{1}{48}+\frac{1}{49}-\frac{1}{50}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)-\left(1+\frac{1}{2}+....+\frac{1}{25}\right)\)\(=\frac{1}{26}+...+\frac{1}{50}\)