Cho a,b là các số dương và x,y khác không thỏa mãn

\(\frac{x^2}{a^2.y^2}\)\(=\)\(\frac{1}{a^2.y^2+b^2.x^2}\)và \(x^2\)+\(y^2\)\(=1\)

CMR:\(\frac{x^{2010}}{a^{1005}}\)+\(\frac{y^{2010}}{b^{1005}}\)\(=\)\(\frac{2}{\left(a+b\right)^{1005}}\)

Tính:

A=\(\frac{7}{3}\).\(\frac{11}{16}\)+\(\frac{10}{3}\).\(\frac{7}{16}\)-\(\frac{7}{6}\).\(\frac{5}{8}\)

B=1+2-3-4+5+6-7-8+.....+2005+2006-2007-2008+2009+2010

C=(1-\(\frac{1}{4}\))(1-\(\frac{1}{9}\))(1-\(\frac{1}{16}\))......(1-\(\frac{1}{100000}\))

D=\(\frac{17\frac{3}{4}.\frac{17}{5}+3\frac{2}{5}.82\frac{1}{4}}{2.34-3.17}\)

E=\(\frac{\frac{2008}{2011}+\frac{2009}{2010}+\frac{2010}{2009}+\frac{2011}{2008}+\frac{2012}{503}}{\frac{1}{2011}+\frac{1}{2010}+\frac{1}{2009}+\frac{1}{2008}}\)

F=(2-\(\frac{2}{1.3}\))+(2-\(\frac{2}{3.5}\))+(2-\(\frac{2}{5.7}\))+.....+(2-\(\frac{2}{2009.2011}\))

\(S=\left(-3\right)^0+\left(-3\right)^1+\left(-3\right)^2+...+\left(-3\right)^{2017}\)

\(P=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}\)

\(Q=\frac{1}{1009}+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2016}+\frac{1}{2017}\)

\(T\text{ÍNH}\)\(T\text{ỔNG}\)\(\left(S,P,Q\right)\)