Question

A = 1 + 1/2 + 1/3 + 1/4 + 1/5 +1/6

CM : 20A chia hết cho 7

Answer 1

=\(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\)

=\(1+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{4}+\frac{1}{5}\right)\)

=\(1+\left(\frac{3}{6}+\frac{2}{6}+\frac{1}{6}\right)+\left(\frac{5}{20}+\frac{4}{20}\right)\)

=\(1+1+\frac{9}{20}\)

=\(2+\frac{9}{20}\)

=\(2\frac{9}{20}\)

Vậy A=\(2\frac{9}{20}\)

Ta có \(20A=20.2\frac{9}{20}=20.\frac{49}{20}=\frac{20.49}{20}=49\)

Mà 49 chia hết cho 7

=>20A chia hết cho 7