Tính : A=\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2017}}{\dfrac{2016}{1}+\dfrac{2015}{2}+\dfrac{2014}{3}+...+\dfrac{1}{2016}}\)
a) Chứng minh rằng: \(\dfrac{1}{6}< \dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+...+\dfrac{1}{100^2}< \dfrac{1}{4}\)
b) Tìm số nguyên a để: \(\dfrac{2a+9}{a+3}+\dfrac{5a+17}{a+3}-\dfrac{3a}{a+3}\) là số nguyên.
1.Tính
\(\left(1-\dfrac{1^2}{100}\right)\left(1-\dfrac{2^2}{100}\right)\left(1-\dfrac{3^2}{100}\right)...\left(1-\dfrac{2018^2}{100}\right)\)
2.S=\(\dfrac{1}{4}+\dfrac{2}{4^2}+\dfrac{3}{4^3}+...+\dfrac{2017}{4^{2017}}\)
Chứng minh rằng S <\(\dfrac{1}{2}\)
CMR:
\(\dfrac{1}{5^3}+\dfrac{1}{6^3}+\dfrac{1}{7^3}+...+\dfrac{1}{2004^3}< \dfrac{1}{40}\)
Tính hoac tinh nhanh neu duoc:
a)\(\left(\dfrac{7}{6}+\dfrac{1}{2}\right):2-2:\left(\dfrac{7}{6}+\dfrac{1}{2}\right)\)
b)\(\left|_{ }-\dfrac{2}{5}+2\right|.\left(\dfrac{1}{3}\right)^3-\dfrac{1}{5}.3+2017^0\)
1. Tính :
a, \(A=\dfrac{\dfrac{1}{3}-\dfrac{5}{2}}{\dfrac{3}{4}-\dfrac{1}{2}}.\dfrac{\dfrac{5}{6}+\dfrac{7}{3}}{1-\dfrac{5}{6}}.\dfrac{\dfrac{-2}{5}+1}{\dfrac{2}{5}-1}\).
b, \(B=\dfrac{\dfrac{1}{3}-\dfrac{4}{5}}{\dfrac{1}{3}+\dfrac{4}{5}}.\dfrac{\dfrac{3}{4}-\dfrac{5}{3}}{\dfrac{3}{4}+\dfrac{5}{3}}:\dfrac{\dfrac{4}{5}-1}{1-\dfrac{2}{3}}\).
\(\dfrac{3}{8}\cdot27\dfrac{1}{5}-51\dfrac{1}{5}\cdot\dfrac{3}{8}+19\)
\(\dfrac{35\dfrac{1}{6}}{\left(\dfrac{-4}{5}\right)}-\dfrac{46\dfrac{1}{6}}{\left(\dfrac{-4}{5}\right)}\)
\(\dfrac{\left(\dfrac{-3}{4}+\dfrac{2}{5}\right)}{\dfrac{3}{7}+\dfrac{\left(\dfrac{3}{5}+\dfrac{-1}{4}\right)}{\dfrac{3}{7}}}\)
Chứng minh rằng:
\(\dfrac{7}{1^3.2^3}+\dfrac{19}{2^3.3^3}+\dfrac{37}{3^3.4^3}+...+\dfrac{29701}{99^3.100^3}< 1\)
10 Thực hiện các phép tính sau:
a) \(\dfrac{-2}{3}+\dfrac{3}{4}-\dfrac{-1}{6}+\dfrac{-2}{5}\) b) \(\dfrac{-2}{3}+\dfrac{-1}{5}+\dfrac{3}{4}-\dfrac{5}{6}-\dfrac{-7}{10}\)
c)\(\dfrac{1}{2}-\dfrac{-2}{5}+\dfrac{1}{3}+\dfrac{5}{7}-\dfrac{-1}{6}+\dfrac{-4}{35}+\dfrac{1}{41}\) ;
d)\(\dfrac{1}{100.99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
