Question

Tìm N biết

                 \(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{N}=\frac{332}{323}\)

Answer 1

\(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{x.\left(x+2\right)}=\frac{332}{323}\)

=>\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{332}{323}\)

=>\(\frac{1}{1}-\frac{1}{x+2}=\frac{332}{323}\)

=>\(\frac{x+2}{x+2}-\frac{1}{x+2}=\frac{332}{323}\)

=>\(\frac{x+1}{x+2}=\frac{332}{323}\)

=>332.(x+2)=323.(x+1)

=>332x+664=323x+323

=>332x-323x=323-664

=>x.(332-323)=-323

=>9x=-323

=>x=-323/9

vậy n=-323/9 .(-323/9+2)=98515/81