Tính:
K = \(\dfrac{1}{1.2.3.4}\)+\(\dfrac{1}{2.3.4.5}\)+......+\(\dfrac{1}{n\left(n+1\right)\left(n+2\right)}\)
M = \(\dfrac{1}{2}\) +\(\dfrac{5}{6}\)+\(\dfrac{11}{12}\)+\(\dfrac{19}{20}\)+\(\dfrac{29}{30}\)+\(\dfrac{41}{42}\)+\(\dfrac{55}{56}\)+\(\dfrac{71}{72}\)+\(\dfrac{89}{90}\)
\(Tìm\) \(x\)∈\(Z\)\(,\) \(biết\)\(:\)
\(a\)) \(\left(x-20\right)+\left(x-19\right)+\left(x-18\right)+...+99+100=100\)
\(b\)) \(213-x.\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2020}}\right):\left(1-\dfrac{1}{2^{2020}}\right)=13\)
Tìm x :
a) \(\left|x+\dfrac{11}{17}\right|+\left|x+\dfrac{2}{17}\right|+\left|x+\dfrac{4}{17}\right|=4x\)
b) \(\left|x+\dfrac{1}{2}\right|+\left|x+\dfrac{1}{6}\right|+\left|x+\dfrac{1}{12}\right|+\left|x+\dfrac{1}{20}\right|+..+\left|x+\dfrac{1}{110}\right|=11x\)
Tính tổng :
a) B = \(\dfrac{1}{5}\) + \(\dfrac{1}{20}\)+ \(\dfrac{1}{44}\) +\(\dfrac{1}{77}\) +\(\dfrac{1}{119}\) + \(\dfrac{1}{170}\) +\(\dfrac{1}{230}\) +\(\dfrac{1}{299}\)
b) C = \(\left(1+\dfrac{1}{1.3}\right)\) \(\left(1+\dfrac{1}{2.4}\right)\) \(\left(1+\dfrac{1}{3.5}\right)\) .....\(\left(1+\dfrac{1}{2014.2016}\right)\)
Tìm x, biết:
a) \(\dfrac{3}{4.7}+\dfrac{3}{7.10}+....+\dfrac{3}{x\left(x+3\right)}=\dfrac{9}{38}\)
b) \(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)
Tìm giá trị nhỏ nhất :
\(D=\left|x-\dfrac{1}{2}\right|+\left|x-\dfrac{1}{3}\right|+\left|x-\dfrac{1}{4}\right|+...+\left|x-\dfrac{1}{2022}\right|\)
Câu hỏi today là a, \(\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{x+\left(x+1\right)}=\dfrac{101}{1540}\)
b,\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{x+\left(x+1\right)}=\dfrac{2020}{2021}\)
Chúc các bn học tốt ❤
Tìm x, biết : \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{1005}{2011}\)
\(\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^{x-2}=\dfrac{1}{216}\)
\(\left[\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^{x-5}\right]^{x-1}=\dfrac{1}{36}\)