\(M=\frac{3}{2}.\left(\frac{2}{11.13}+\frac{2}{13.15}+......+\frac{2}{97.99}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+.....+\frac{1}{97}-\frac{1}{99}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{11}-\frac{1}{99}\right)=\frac{3}{2}.\frac{8}{99}=\frac{4}{33}\)
M= \(\frac{3}{11\cdot13}+\frac{3}{13\cdot15}+\frac{3}{15\cdot17}+...+\frac{3}{97\cdot99}\)
=\(\frac{3}{2}\cdot\left(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+\frac{2}{15\cdot17}+...+\frac{2}{97\cdot99}\right)\)
=\(\frac{3}{2}\cdot\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}\right)\)
=\(\frac{3}{2}\cdot\left(\frac{1}{11}-\frac{1}{99}\right)\)
=\(\frac{3}{2}\cdot\frac{8}{99}\)
= \(\frac{4}{33}\)
M=\(3\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+....+\frac{1}{97}-\frac{1}{99}\right)\)
M=3(\(\frac{1}{11}-\frac{1}{99}\))
M=3.8/99
M=8/33
M=3/11.13 + 3/13.15 + 3/15.17 + .... + 3/97.99
M=3/2 .(2/11.13 + 2/13.15 + 2/15.17 +... + 2/97.99)
M=3/2.(1/11-1/13+1/13-1/15+1/15-1/17+...+1/97-1/99)
M=3/2.(1/11-1/99)
M=3/2.(9/99-1/99)
M=3/2.8/99
M=4/33
Vậy M =4/33
\(M=\frac{3}{11.13}+\frac{3}{13.15}+\frac{3}{15.17}+...+\frac{3}{97.99}\)
\(M=\frac{3}{2}\times\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{97.99}\right)\)
\(M=\frac{3}{2}\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(M=\frac{3}{2}\times\left(\frac{1}{11}-\frac{1}{99}\right)\)
\(M=\frac{3}{2}\times\frac{8}{99}\)
\(M=\frac{4}{33}\)
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