B = 2/15 + 2/35 + 2/63 +...+ 2/399
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20 tháng 2 2022
\(\frac{2}{15}+\frac{2}{35}+...+\frac{2}{399}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}\)
\(=\frac{2}{7}\)
HT
PQ
2
4 tháng 8 2019
\(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(B=\frac{2}{3×5}+\frac{2}{5×7}+\frac{2}{7×9}+...+\frac{2}{19×21}\)
\(B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{19}-\frac{1}{21}\)
\(B=\frac{1}{3}-\frac{1}{21}\)
\(B=\frac{2}{7}\)
4 tháng 8 2019
A=\(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{10}\)+\(\frac{1}{15}\)+...+\(\frac{1}{66}\)
A=\(\frac{1}{1\cdot3}\) +\(\frac{1}{2\cdot3}\) +\(\frac{1}{2\cdot5}\)+...+\(\frac{1}{6\cdot11}\)
A=\(\frac{1}{1}-\frac{1}{3}+\frac{1}{2}-\frac{1}{3}+\frac{1}{2}-\frac{1}{5}+...+\frac{1}{6}-\frac{1}{11}\)
A=\(\frac{1}{1}-\frac{1}{11}\)
=>A=\(\frac{10}{11}\)
B=\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
2B=\(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{19\cdot21}\)
2B=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
2B=\(\frac{1}{3}-\frac{1}{21}\)
2B=\(\frac{2}{7}\)
B=\(\frac{2}{7}:2\)
=>B=\(\frac{1}{7}\)
TL
3
TC
13 tháng 3 2023
`A =2/15 +2/35 +2/63 +... +2/339`
`= 2/(3.5) +2/(5.7) + 2/(7.9) + ...+2/(19.21)`
`= 1/3 -1/5 +1/5 -1/7 +1/7 -1/9 +... 1/19 -1/21`
`= 1/3 -1/21 = 7/21 -1/21`
`=6/21 = 2/7`
LH
4 tháng 8 2016
\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\)
\(A=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)
VA
26 tháng 7 2016
\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+..+\frac{2}{399}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}=\frac{7}{21}-\frac{1}{21}=\frac{6}{21}=\frac{2}{7}\)
Ủng hộ mk nha !!! ^_^
TT
1
20 tháng 1 2017
Ta có \(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(=2.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\right)\)
\(=2.\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{2}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(=\frac{2}{7}\)
Vậy \(B=\frac{2}{7}\)
CC
4
3 tháng 8 2016
\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{19\times21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}\)
\(=\frac{7}{21}-\frac{1}{21}\)
\(=\frac{6}{21}\)
3 tháng 8 2016
Rút gọn kết quả là \(\frac{2}{7}\), k mk nha mk trả lời đầu tiên đó
2 tháng 8 2015
a.\(A=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\)
\(=\frac{1}{3}-\frac{1}{111}=\frac{37}{111}-\frac{1}{111}=\frac{36}{111}=\frac{12}{37}\)
Vậy A=\(\frac{12}{37}\)
b.\(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}=\frac{7}{21}-\frac{1}{21}=\frac{6}{21}=\frac{2}{7}\)
Vậy \(B=\frac{2}{7}\)
c.\(C=\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)
\(\Rightarrow C.\frac{1}{2}=\left(\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\right).\frac{1}{2}\)
\(=\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\)
\(=\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{15.16}\)
\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\)
\(=\frac{1}{4}-\frac{1}{16}=\frac{4}{16}-\frac{1}{16}=\frac{3}{16}\)
Vậy \(C=\frac{3}{16}\)
HT
2 tháng 8 2015
A = \(\frac{4}{3.7}+\frac{4}{7.9}+...+\frac{4}{107.111}\)
A = \(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{107}-\frac{1}{111}\)
A = \(\frac{1}{3}-\frac{1}{111}\)=\(\frac{12}{37}\)
2 câu sau tương tự. Mik ngại làm lắm -_-
\(B=\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{29.31}\)
\(B=2.\left(\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{29.31}\right)\)
\(B=2.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{29}-\frac{1}{31}\right)\)
\(B=2.\left(\frac{1}{3}-\frac{1}{31}\right)\)
\(B=2.\frac{28}{93}\)
\(B=\frac{56}{93}\)
k cho mình nha chúc bạn học tốt