Question

\(\dfrac{y}{2022}-\dfrac{1}{10}-\dfrac{1}{15}-\dfrac{1}{21}-...-\dfrac{1}{120}=\dfrac{5}{8}\)

Answer 1

Ta có: \(\frac{y}{2022}-\frac{1}{10}-\frac{1}{15}-\frac{1}{21}-\cdots-\frac{1}{120}=\frac58\)

=>\(\frac{y}{2022}-\frac{2}{20}-\frac{2}{30}-\frac{2}{42}-\cdots-\frac{2}{240}=\frac58\)

=>\(\frac{y}{2022}-2\left(\frac{1}{20}+\frac{1}{30}+\cdots+\frac{1}{240}\right)=\frac58\)

=>\(\frac{y}{2022}-2\times\left(\frac14-\frac15+\frac15-\frac16+\cdots+\frac{1}{15}-\frac{1}{16}\right)=\frac58\)

=>\(\frac{y}{2022}-2\times\left(\frac14-\frac{1}{16}\right)=\frac58\)

=>\(\frac{y}{2022}-2\times\frac{3}{16}=\frac58\)

=>\(\frac{y}{2022}=\frac58+\frac38=1\)

=>y=2022