Cho A=\(\dfrac{1}{4}\)+\(\dfrac{1}{9}\)+\(\dfrac{1}{16}\)+....+\(\dfrac{1}{2014^2}\).Hãy chứng tỏ A<\(\dfrac{3}{4}\)

bài 1 :tìm x biết

\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+\(\dfrac{1}{4.5}\)+...+\(\dfrac{1}{x.\left(x+1\right)}\)=\(\dfrac{9}{20}\)

bài 2:tính

\(\dfrac{1}{4.5}\)+\(\dfrac{2}{5.7}\)+\(\dfrac{3}{7.10}\)+\(\dfrac{4}{10.14}\)+\(\dfrac{5}{14.19}\)+\(\dfrac{6}{19.25}\)

bài 3: tính

\(\left(1+\dfrac{1}{10}\right)\)\(\left(1+\dfrac{1}{11}\right)\)\(\left(1+\dfrac{1}{12}\right)\)...\(\left(1+\dfrac{1}{100}\right)\)