Question

CHO a/b =1/2+1/3+1/4+...+1/9

CMR ạ chia het cho 11

Answer 1

\(\frac{a}{b}=\left(\frac{1}{2}+\frac{1}{9}\right)+\left(\frac{1}{3}+\frac{1}{8}\right)+...+\left(\frac{1}{5}+\frac{1}{6}\right)\)

\(\frac{a}{b}=\frac{11}{2\cdot9}+\frac{11}{3\cdot8}+...+\frac{11}{5\cdot6}\)

\(\frac{a}{b}=11\cdot\left(\frac{1}{2\cdot9}+\frac{1}{3\cdot8}+...+\frac{1}{5\cdot6}\right)\)

mà 11 là số nguyên tố 

=> A chia hết cho 11

Answer 2

$\frac{a}{b}=\left(\frac{1}{2}+\frac{1}{9}\right)+\left(\frac{1}{3}+\frac{1}{8}\right)+...+\left(\frac{1}{5}+\frac{1}{6}\right)$ab =(12 +19‍ )+(13 +18 )+...+(15 +16 )

\(\frac{a}{b}=\frac{11}{2\cdot9}+\frac{11}{3\cdot8}+...+\frac{11}{5\cdot6}\)

\(\frac{a}{b}=11\cdot\left(\frac{1}{2\cdot9}+\frac{1}{3\cdot8}+...+\frac{1}{5\cdot6}\right)\)

mà 11 là số nguyên tố 

=> A chia hết cho 11

Answer 3

=> a chia het cho 11