1) Tính:

\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+........+\frac{2}{97.99}\)

\(B=\frac{\left(2^3.5.7\right).\left(5^2.7^3\right)}{\left(2.5.7^2\right)^2}\)

\(C=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.......\frac{1}{97.99}\)
 

\(D=\left(\frac{\frac{12}{1}-\frac{12}{5}-\frac{12}{487}}{\frac{4}{1}-\frac{4}{5}-\frac{4}{487}}\right):\left(\frac{\frac{5}{1}+\frac{5}{17}+\frac{5}{37}}{\frac{6}{1}+\frac{6}{17}+\frac{6}{37}}\right).\frac{505}{1818}\)

2) So sánh:
a)\(\frac{2008}{2009}+\frac{2009}{2010}\) và \(\frac{2008+2009}{2009+2010}\)

b) \(\frac{12}{23}\) và \(\frac{1212}{2323}\)

Giúp mình nha. Mai mình kiểm tra 45'.

a, Tính : \(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)

b, Tính : \(P=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}}{\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{1}{2011}}\)

c, Tính : \(\frac{\left(1+2+3+...+99+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+...+99-100}\)

Tính:

a.A =  \(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)

b. B = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}}{\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{1}{2011}}\)

c. C = \(\frac{\left(1+2+3+...+99+100\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right).\left(63.1,2-21.3,6\right)}{1-2+3-4+...+99-100}\)

1.Tính tổng

\(S=\left(\frac{-1}{7}\right)^0+\left(\frac{-1}{7}\right)^1+\left(\frac{-1}{7}\right)^2+...+\left(\frac{-1}{7}\right)^{2007}\)

2.Tìm x

\(5^x+5^{x+2}=650\)

3.CMR

\(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)

4.  Cho  \(A=\frac{1}{2010}+\frac{2}{2009}+\frac{3}{2008}+...+\frac{2009}{2}+\frac{2010}{1}\)

  \(B=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2010}+\frac{1}{2011}\)

So sánh A và B