Question

tính nhanh A= 2/3*7+3/7*13+4/13*21+5/21*31+6/31*43+7/43*57

Answer 1

Ta có: \(A=\frac{2}{3\times7}+\frac{3}{7\times13}+\frac{4}{13\times21}+\frac{5}{21\times31}+\frac{6}{31\times43}+\frac{7}{43\times57}\)

\(=\frac12\times\left(\frac{4}{3\times7}+\frac{6}{7\times13}+\frac{8}{13\times21}+\frac{10}{21\times31}+\frac{12}{31\times43}+\frac{14}{43\times57}\right)\)

\(=\frac12\times\left(\frac13-\frac17+\frac17-\frac{1}{13}+\frac{1}{13}-\frac{1}{21}+\frac{1}{21}-\frac{1}{31}+\frac{1}{31}-\frac{1}{43}+\frac{1}{43}-\frac{1}{57}\right)\)

\(=\frac12\times\left(\frac13-\frac{1}{57}\right)=\frac12\times\frac{18}{57}=\frac12\times\frac{6}{19}=\frac{3}{19}\)

Answer 2

=12387