\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+............+\frac{2}{2004\times2005}\)

giúp mình nhé

\(a=\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+......+\frac{1}{2003\times2005}\)

BÀI 1 : So sánh 

A = \(\frac{17^{18}+1}{17^{19}+1}\)và B = \(\frac{17^{17}+1}{17^{18}+1}\) So sánh A và B

\(\frac{n}{n+3}\)và \(\frac{n+1}{n+2}\)

\(\frac{2003\times2004-1}{2003\times2004}\)và \(\frac{2004\times2005-1}{2004\times2005}\)

chứng minh rằng \(\frac{A}{B}\) là số nguyên

A = \(\frac{1}{1\times2}+\frac{1}{3\times4}+...+\frac{1}{2005\times2006}\)

B = \(\frac{1}{1004\times2006}+\frac{1}{1005\times2005}+...+\frac{1}{2006\times1004}\)

Tính hợp lí:

A=\(\frac{5}{12\times17}+\frac{35}{17\times18}-\frac{39}{18\times21}+\frac{30}{21\times72}\)

B=\(\frac{767676\times31-626262\times38}{1^2+2^3+3^4+......+99^{100}}\)

tính giá trị biểu thức: A=\(\frac{5}{12\times17}+\frac{35}{17\times18}-\frac{39}{18\times21}+\frac{30}{21\times72}\)

Bài 9: Tìm x biết:

a, \(x+\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+....+\frac{4}{41\times45}=\frac{-37}{45}\)

b, \(x-\frac{20}{11\times13}-\frac{20}{13\times15}-\frac{20}{15\times17}-....-\frac{20}{53\times55}=\frac{3}{11}\)

c, \(\frac{1}{21}+\frac{1}{21}+\frac{1}{36}+.....+\frac{2}{x+\left(x+1\right)}=\frac{2}{9}\)

Tính các giá trị biểu thức sau :

A=\(1+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2006}}\)

B=\(-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{100}}-\frac{1}{3^{101}}\)

C=\(\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1}{1\cdot999}+\frac{1}{3\cdot997}+...+\frac{1}{997\cdot3}+\frac{1}{999\cdot1}}\)

Tính giá trị các biểu thức sau:

 a,A=\(\frac{2}{3}+\frac{5}{6}:5-\frac{1}{18}.\left(-3\right)^2\)

 b,B=\(3.\left(5.\left(\left(5^2+2^3\right):11\right)-16\right)+2015\)

 c,C=\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{2014.2016}\right)\)