Question

\(B=\frac{4}{7\cdot31}+\frac{6}{7\cdot41}+\frac{9}{10\cdot41}+\frac{7}{10\cdot57}\)

Answer 1

\(B=\frac{4}{7\cdot31}+\frac{6}{7\cdot41}+\frac{9}{10\cdot41}+\frac{10}{10\cdot57}\)

B/5 = 4/5*7*31 + 6/5*7*41 + 9/5*10*410+7/5*10*57

B/5=4/31*35+6/35*41+9/41*50+7/50*57

B/5= 1/31-1/35+1/35-1/41+1/41-1/50+1/50-1/57

B/5=1/31-1/57

B/5=26/1767

B=130/1767

Vậy B = 130/1767

Answer 2

Bạn Vũ Thành Huy giải hay wá :) Cảm ơn bạn.

Answer 3

\(B=\frac{4}{7.31}+\frac{6}{7.41}+\frac{9}{10.41}+\frac{7}{10.57}\)

\(B=\frac{5}{5}.\left(\frac{4}{7.31}+\frac{6}{7.41}+\frac{9}{10.41}+\frac{7}{10.57}\right)\)

\(B=5\left(\frac{4}{5.7.31}+\frac{6}{5.7.41}+\frac{9}{5.10.41}+\frac{7}{5.10.57}\right)\)

\(B=5\left(\frac{4}{35.31}+\frac{6}{35.41}+\frac{9}{50.41}+\frac{7}{50.57}\right)\)

\(B=5\left(\frac{4}{31.35}+\frac{6}{35.41}+\frac{9}{41.50}+\frac{7}{50.57}\right)\)

\(B=5\left(\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{41}+\frac{1}{41}-\frac{1}{50}+\frac{1}{50}-\frac{1}{57}\right)\)

\(B=5.\left(\frac{1}{31}-\frac{1}{57}\right)\)

\(B=5.\frac{26}{1767}\)

\(B=\frac{130}{1767}\)