tham khảo
A = 3/1.8 + 3/8.15 + 3/15.22 + ... + 3/106.113
A = 3/7 ( 7/1.8 + 7/8.15 + 7/15.22 +...+ 7/106.113)
A = 3/7 (8-1/1.8 + 15-8/8.15 + 22-15/15.22 +...+ 113-106/106.113)
A = 3/7 ( 1 - 1/8 + 1/8 - 1/15 + 1/15 - 1/22 + 1/106 - 1/113
A = 3/7 (1 - 1/113)
A = 48/113
B = 25/50.55 + 25/55.60 +...+ 25/95.100
B = 5 (5/50.55 + 5/55.60 +...+ 5/95.100)
B = 5 ( 55-50/50.55 + 60-55/55.60 +...+ 100-95/95.100)
B = 5 ( 1/50 - 1/55 + 1/55 - 1/60 +...+ 1/95 - 1/100)
mình cũng chia lm 2 vế
Đặt `X = 3/(1.8) + ... + 3/(106.113)`
`Y = 25/(50.55) + ... + 25/(95.100)`
`=> 7/3 X = 1/1 - 1/8 + ... + 1/106 - 1/113`
`=> 7/3X = 112/113`
`=> X = 112/113 : 7/3`
`=> X = 336/791`.
`1/5Y = 1/50 - 1/55 + .... + 1/95 - 1/100`
`1/5Y = 1/50 - 1/100`
`1/5Y = 1/100`
`Y = 1/100 : 1/5 = 1/20`.
`=> X - Y = A = 336/791 - 1/20 = 847/2260`.
tham khảo cách làm trên mạng
ta chia A thành hai vế
B=\(\dfrac{3}{1.8}+\dfrac{3}{8.15}+....+\dfrac{3}{16.113}\)
\(\dfrac{7}{3}B=\dfrac{7}{3}\left(\dfrac{3}{1.8}\right)+\dfrac{7}{3}\left(\dfrac{3}{8.15}\right)+...+\dfrac{7}{3}\left(\dfrac{3}{106.113}\right)\)
\(\dfrac{7}{3}B=\dfrac{7}{3}\left(\dfrac{3}{1.8}+\dfrac{3}{8.15}+...+\dfrac{3}{106.113}\right)\)
\(\dfrac{7}{3}B=\dfrac{7}{1.8}+\dfrac{7}{8.15}+...+\dfrac{7}{106.113}\)
\(\dfrac{7}{3}B=\dfrac{7}{1}-\dfrac{7}{8}+\dfrac{7}{8}-\dfrac{7}{15}+...+\dfrac{7}{106}-\dfrac{7}{113}\)
\(\dfrac{7}{3}B=7-\dfrac{7}{113}=\dfrac{784}{113}\)
→\(B=\dfrac{784}{113}:\dfrac{7}{3}=\dfrac{336}{113}\)
C=\(\dfrac{25}{50.55}+\dfrac{25}{55.60}+....+\dfrac{25}{95.100}\)
\(\dfrac{1}{5}C=\dfrac{1}{5}\left(\dfrac{25}{50.55}\right)+\dfrac{1}{5}\left(\dfrac{25}{55.60}\right)+...+\dfrac{1}{5}\left(\dfrac{25}{95.100}\right)\)
\(\dfrac{1}{5}C=\dfrac{1}{5}\left(\dfrac{25}{50.55}+\dfrac{25}{55.60}+...+\dfrac{25}{95.100}\right)\)
\(\dfrac{1}{5}C=\dfrac{5}{50.55}+\dfrac{5}{55.60}+...+\dfrac{5}{95.100}\)
\(\dfrac{1}{5}C=\dfrac{5}{50}-\dfrac{5}{55}+\dfrac{5}{55}+\dfrac{5}{60}+...+\dfrac{5}{95}-\dfrac{5}{100}\)
\(\dfrac{1}{5}C=\dfrac{5}{50}-\dfrac{5}{100}=\dfrac{1}{10}-\dfrac{1}{20}=\dfrac{1}{20}\)
→\(C=\dfrac{1}{20}:\dfrac{1}{5}=\dfrac{1}{4}\)
Vậy A=B-C=\(\dfrac{336}{113}-\dfrac{1}{4}=\dfrac{1231}{452}\)
