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=2/10+3/10+4/10+......+13/10
=\(\frac{2+3+4+......+13}{10}\)
=90/10=9
k cho mình nha
A=\(\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{13}-\frac{1}{14}\)=\(\frac{1}{7}-\frac{1}{14}\)=\(\frac{1}{14}\)
B=0
\(\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+\frac{1}{13.14}\)
\(=\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}\)
\(=\frac{1}{7}-\frac{1}{14}=\frac{1}{14}\)
\(\frac{x+10}{90}+\frac{x+20}{80}+\frac{x+30}{70}+\frac{x+40}{60}+\frac{x+50}{50}=-5\)
<=> \(\frac{x+10}{90}+1+\frac{x+20}{80}+1+\frac{x+30}{70}+1+\frac{x+40}{60}+1+\frac{x+50}{50}+1=0\)
<=> \(\frac{x+100}{90}+\frac{x+100}{80}+\frac{x+100}{70}+\frac{x+100}{60}+\frac{x+100}{50}=0\)
<=> \(\left(x+100\right)\left(\frac{1}{90}+\frac{1}{80}+\frac{1}{70}+\frac{1}{60}+\frac{1}{50}\right)=0\)
<=> x + 100 = 0
<=> x = -100
Vậy x = -100
\(A=\frac{10^2}{20^2}+\frac{20^2}{30^2}=\frac{25}{36}\)
\(B=\frac{10^2+20^2}{20^2+30^2}=\frac{5}{13}\)
ta đổi :\(\frac{25}{36}\)và \(\frac{5}{13}\)ra thành cùng mẫu
suy ra bằng \(\frac{325}{468}\)và \(\frac{180}{468}\)
vì \(\frac{325}{468}>\frac{180}{468}\)nên \(A>B\)
đúng thì nhớ k đấy nhé
\(M=\frac{15}{56}+\frac{1}{14}+\frac{1}{26}+\frac{5}{208}\)
\(M=\frac{15}{56}+\frac{4}{56}+\frac{8}{208}+\frac{5}{208}\)
\(M=\frac{19}{56}+\frac{13}{208}=\frac{45}{112}\)
a)
\(=\frac{7\cdot7\cdot8\cdot8\cdot9\cdot9\cdot10\cdot10\cdot11\cdot11}{6\cdot8\cdot7\cdot9\cdot8\cdot10\cdot9\cdot11\cdot10\cdot12}\)
\(=\frac{7\cdot11}{6\cdot12}\)
\(=\frac{77}{72}\)
b)
\(=1+\frac{1}{6}+1+\frac{1}{12}+1+\frac{1}{20}+1+\frac{1}{30}+1+\frac{1}{42}+1+\frac{1}{56}\)
\(=6+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)
\(=6+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)
\(=6+\frac{1}{2}-\frac{1}{8}\)
\(=6+\frac{3}{8}\)
\(=\frac{51}{8}\)
Chia thành...a và b nhé.
Bg
a)Ta có: \(\frac{49}{48}.\frac{64}{63}.\frac{81}{80}.\frac{100}{99}.\frac{121}{120}\)
= \(\frac{49.64.81.100.121}{48.63.80.99.120}\)
= \(\frac{7.7.8.8.9.9.10.10.11.11}{6.8.7.9.8.10.9.11.10.12}\)
= \(\frac{7.11}{6.12}\) (chịt tiêu trên dưới)
= \(\frac{77}{72}\)
b) Ta có: \(\frac{7}{6}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}\)
Có 6 số hạng (đếm)
= \(1+\frac{1}{6}+1+\frac{1}{12}+1+\frac{1}{20}+1+\frac{1}{30}+1+\frac{1}{42}+1+\frac{1}{56}\)
= \(1+1+...+1+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)
= \(1.6+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
= \(6+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
= \(6+\frac{1}{2}-\frac{1}{8}\)
= \(\frac{13}{2}-\frac{1}{8}\)
= \(\frac{51}{8}\)
Hơi dài....