CMR: S = \(\dfrac{1}{4}+\dfrac{2}{4^2}+\dfrac{3}{4^3}+\dfrac{4}{4^4}+...+\dfrac{2016}{4^{2016}}+\dfrac{2017}{4^{2017}}\)< \(\dfrac{1}{2}\)
Tìm x\(\in\) Z, biết: \(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{2}{x.\left(x+1\right)}\) =\(\dfrac{2014}{2016}\)
Cc bn ơi giúp mk vs mk đg rất gấp!!!!!!!
Cho tổng T = \(\dfrac{2}{2^1}\)+\(\dfrac{3}{2^2}\)+\(\dfrac{4}{2^3}\)+...+\(\dfrac{2016}{2^{2015}}\)+\(\dfrac{2017}{2^{2016}}\)
So sánh T với 3
Tính
A=\(\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{6}-1\right)\left(\dfrac{1}{10}-1\right)\left(\dfrac{1}{15}-1\right)\left(\dfrac{1}{21}-1\right)\left(\dfrac{1}{28}-1\right)\left(\dfrac{1}{36}-1\right)\)
B=\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)........\left(1-\dfrac{1}{10^2}\right)\)
C=\(1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+..........+\dfrac{1}{2^{2016}}\)
Giúp mk nha!Cảm ơn rất nhìu!
Các bn ơi giúp mk vs nha.
So sánh:
A= \(\dfrac{10^{2015}+1}{10^{2016}+1}\) và B= \(\dfrac{10^{1016}+1}{10^{2017}+1}\)
Các bn ơi giúp mk vs nha
Cho minh hoi bai nay vs:
Chung to S=\(\dfrac{1}{4}\)+\(\dfrac{2}{4}\)+...+\(\dfrac{10}{4}\)<14
Chung to S=\(\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{19}< 2\)
Chung to S=\(\dfrac{1}{10}+\dfrac{1}{4}+...+\dfrac{1}{100}>1\)
a) A = \(\left(\dfrac{1}{1009}+\dfrac{1}{1010}+...+\dfrac{1}{2015}+\dfrac{1}{2016}\right):\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)
b) B = \(\dfrac{5x^2+3y^2}{10x^2-3y^2}\) biết \(\dfrac{x}{3}=\dfrac{y}{5}\)
Các bn ơi giúp mk vs nha mấy bn!!
Câu 1: Tìm x, biết
a, x = \(\dfrac{1}{4}\) + \(\dfrac{2}{13}\)
b, \(\dfrac{x}{3}\) = \(\dfrac{2}{3}\) + \(\dfrac{-1}{7}\) +
Câu 3: Tính nhanh:
a, \(\dfrac{-2}{5}\) +\(\dfrac{3}{-4}\) + \(\dfrac{6}{7}\) + \(\dfrac{3}{4}\) + \(\dfrac{2}{5}\)
b, \(\dfrac{7}{15}\) + \(\dfrac{4}{-9}\) + \(\dfrac{-2}{11}\) + \(\dfrac{8}{15}\) + \(\dfrac{-5}{9}\)
c, \(\dfrac{-5}{7}\) + \(\dfrac{5}{13}\) +\(\dfrac{-20}{41}\) + \(\dfrac{8}{13}\) + \(\dfrac{-21}{41}\)
So sánh A vs \(\dfrac{3}{4}\)
Cho A= \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+......+\dfrac{1}{200^2}\)