Question

[Châu Anh Trần]

b, B= 5/15+ 5/35+ 5/63+ 5/99+...+ 5/ 323+ 5/399

Ghi rõ các bước làm giúp mk
SOS

Answer 1

[Minh Hồng]

\(B=\dfrac{5}{15}+\dfrac{5}{35}+\dfrac{5}{63}+\dfrac{5}{99}+...+\dfrac{5}{323}+\dfrac{5}{399}\\ =\dfrac{5}{3\times5}+\dfrac{5}{5\times7}+\dfrac{5}{7\times9}+\dfrac{5}{9\times11}+...+\dfrac{5}{17\times19}+\dfrac{5}{19\times21}\\ =\dfrac{5}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{17}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{21}\right)\\ =\dfrac{5}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{21}\right)\\ =\dfrac{5}{2}\times\dfrac{2}{7}=\dfrac{5}{7}\)

Answer 2

[Nguyễn Thị Thương Hoài]

B = \(\dfrac{5}{15}\)+ \(\dfrac{5}{35}\)+ \(\dfrac{5}{63}\) + \(\dfrac{5}{99}\)+.......+\(\dfrac{5}{323}\)+ \(\dfrac{5}{399}\)

B = \(\dfrac{5}{3.5}\) + \(\dfrac{5}{5.7}\)+ \(\dfrac{5}{7.9}\)+ \(\dfrac{5}{9.11}\)+......+ \(\dfrac{5}{17.19}\)+\(\dfrac{5}{19.21}\)

B = \(\dfrac{5}{2}\)(\(\dfrac{2}{3.5}\)+ \(\dfrac{2}{5.7}\)+ \(\dfrac{2}{7.9}\)+ \(\dfrac{2}{9.11}\)+.....+\(\dfrac{2}{17.19}\)+ \(\dfrac{2}{19.21}\))

B =\(\dfrac{5}{2}\) (\(\dfrac{1}{3}\)- \(\dfrac{1}{5}\)+ \(\dfrac{1}{5}\)- \(\dfrac{1}{7}\)+ \(\dfrac{1}{7}\)- \(\dfrac{1}{9}\)+ \(\dfrac{1}{9}\)- \(\dfrac{1}{11}\) +......+\(\dfrac{1}{17}\)-\(\dfrac{1}{19}\)+ \(\dfrac{1}{19}\)- \(\dfrac{1}{21}\))

B = \(\dfrac{5}{2}\)( \(\dfrac{1}{3}\) - \(\dfrac{1}{21}\))

B = \(\dfrac{5}{2}\) . \(\dfrac{2}{7}\)

B =5/7