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\(\frac{2,4\times1994\times2+1,6\times3996\times3+1,2\times4010\times4}{3+7+11+...+95+99-275}\)
\(=\frac{0,2\times6\times2\times2\times997\times2+0,2\times8\times6\times666\times3+0,2\times6\times2\times2005\times4}{\left(99+3\right)\times49:2-275}\)
\(=\frac{0,2\times6\times8\times997+0,2\times8\times6\times666\times3+0,2\times6\times8\times2005}{2499-275}\)
\(=\frac{0,2\times6\times8\times\left(997+666\times3+2005\right)}{2224}\)
\(=\frac{0,2\times2\times3\times8\times\left(997+1998+2005\right)}{8\times2\times0,2\times695}\)
\(=\frac{3\times\left(2995+2005\right)}{695}\)
\(=\frac{3\times5000}{695}=\frac{3\times1000\times5}{5\times139}\)
\(=\frac{3\times1000}{139}=\frac{3000}{139}\)
B=2/1.3 + 2/3.5 + 2/5.7 +...+ 2/299.301
B=1-1/3+1/3-1/5+1/5-1/7+...+1/299-1/301=1-1/301=300/301
\(Ta có: \frac{2}{3}=\frac{1}{1}-\frac{1}{3}\);
\(\frac{2}{15}=\frac{1}{3}-\frac{1}{5}\);
\(\frac{2}{35}=\frac{1}{5}-\frac{1}{7}\) ; ... ; \(\frac{2}{89999}=\frac{1}{299}-\frac{1}{301}\).
=> B= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{299}-\frac{1}{301}\)
=> B=\(\frac{1}{1}-\frac{1}{301}\)
=> B=\(\frac{300}{301}\)
\(\frac{4,8\left(1994+3996+4010\right)}{\left(\frac{99-3}{4}+1\right)\left(\frac{99+3}{2}\right)-11.25}=\frac{48000}{25.51-11.25}=\frac{48000}{1000}=48\)