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1/5x8 + 1/8x11 + 1/11x14 + ... + 1/xx(x+3) = 101/1540
1/3 x (3/5x8 + 3/8x11 + 3/11x14 + ... + 3/xx(x+3) = 101/1540
1/3 x (1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + ... + 1/x - 1/x+3) = 101/1540
1/3 x (1/5 - 1/x+3) = 101/1540
1/5 - 1/x+3 = 101/1540 : 1/3
1/5 - 1/x+3 = 303/1540
1/x+3 = 1/5 - 303/1540
1/x+3 = 1/308
=> x+3=308
=> x=308-3=305
vậy x=305
1/5x8 + 1/8x11 + 1/11x14 + ... + 1/xx(x+3) = 101/1540
1/3 x (3/5x8 + 3/8x11 + 3/11x14 + ... + 3/xx(x+3) = 101/1540
1/3 x (1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + ... + 1/x - 1/x+3) = 101/1540
1/3 x (1/5 - 1/x+3) = 101/1540
1/5 - 1/x+3 = 101/1540 : 1/3
1/5 - 1/x+3 = 303/1540
1/x+3 = 1/5 - 303/1540
1/x+3 = 1/308
=> x+3=308
=> x=308-3=305
vậy x=305
\(\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\right)\times y=\frac{2}{3}\)
\(\frac{1}{2}\times\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\times y=\frac{2}{3}\)
\(\frac{1}{2}\times\left(\frac{1}{1}-\frac{1}{11}\right)\times y=\frac{2}{3}\)
\(\frac{1}{2}\times\frac{10}{11}\times y=\frac{2}{3}\)
\(\frac{5}{11}\times y=\frac{2}{3}\) => \(y=\frac{2}{3}:\frac{5}{11}=\frac{2}{3}\times\frac{11}{5}=\frac{22}{15}\)
2/
a) \(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}\)
\(=\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{17}-\frac{1}{21}\right)\)
\(=1-\frac{1}{21}=\frac{20}{21}\)
b) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot..\cdot\frac{2016}{2017}\)
\(=\frac{1}{2017}\)
c) \(A=2000-5-5-5-..-5\)(có 200 số 5)
\(A=2000-\left(5\cdot200\right)\)
\(A=2000-1000\)
\(A=1000\)
(4/1*3+4/3*5+4/5*7+4/7*9)*10-x=0
=4*2/1*3+4*2/3*5+4*2/5*7+4*2/7*9
=1/1+1/3+1/5+1/7+1/9
=1/1-1/9
=8/9
8/9*10-x=0
89-x=0
x=89-0
x=89
\(x\times\left(\frac{2015}{8\times9}+\frac{1925}{9\times10}+\frac{1795}{10\times11}+\frac{1629}{11\times12}+6\right)=\frac{1}{24}\)
=> \(x\times\left(\frac{2015}{72}+\frac{1925}{90}+\frac{1795}{110}+\frac{1629}{132}+6\right)=\frac{1}{24}\)
=> \(x\times84\frac{3}{88}=\frac{1}{24}\Rightarrow x=\frac{1}{24}:\frac{7395}{88}=\frac{1}{24}\times\frac{88}{7395}=\frac{88}{177480}=\frac{11}{22185}\)