1) Không dùng máy tính hãy so sánh:
A=\(\dfrac{2016}{2017}+\dfrac{2017}{2018}+\dfrac{2018}{2019}+\dfrac{2019}{2006}\) với 4
2) So sánh A và B biết:
A=\(\left(100^{99}+99^{99}\right)^{100}\)
B=\(\left(100^{100}+99^{100}\right)^{99}\)
3) Chứng tỏ rằng:
\(\left(2003^n+1\right)\left(2003^n+2\right)⋮6\forall n\in N\)
A= \(\left(\dfrac{1}{2}-1\right)\)\(\left(\dfrac{1}{3}-1\right)\).........\(\left(\dfrac{1}{10}-1\right)\). So sánh A với \(\dfrac{-1}{9}\)
B= \(\left(\dfrac{1}{4}-1\right)\)\(\left(\dfrac{1}{9}-1\right)\)...........\(\left(\dfrac{1}{100}-1\right)\). So sánh B với \(\dfrac{-11}{21}\)
1) Cho A= \(\dfrac{1}{\sqrt{100}}+\dfrac{1}{\sqrt{101}}+\dfrac{1}{\sqrt{102}}+\dfrac{1}{\sqrt{103}}+\dfrac{1}{\sqrt{104}}\)
và B= \(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{4^2}\right)....\left(1-\dfrac{1}{100^2}\right)\)
So sánh A và B.
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\). CMR:\(\dfrac{\left(a^{2018}+b^{2018}\right)^{2019}}{\left(c^{2018}+d^{2018}\right)^{2019}}=\dfrac{\left(a^{2019}-b^{2019}\right)^{2020}}{\left(c^{2019}+d^{2019}\right)^{2020}}\)
HELP ME!!!!!!! Mình cần gấp mai mình lộp bài rùi
Câu 1 : Tìm GTLN
a) \(A=\dfrac{2003}{\left(x-2\right)^2+\left(x-y\right)^6+3}\)
b) \(B=3-\left(2x+\dfrac{1}{3}\right)^6\)
c) \(C=\dfrac{x^{2016}+2017}{x^{2016}+2015}\)
1 tính
a, \(-\dfrac{2}{3}-\left(\dfrac{-2}{5}\right)-\dfrac{7}{10}\)
b, \(\dfrac{-5}{9}.\left(\dfrac{3}{10}-\dfrac{2}{5}\right)\)
c, \(\left(\dfrac{11}{24}:\dfrac{55}{36}\right).\dfrac{10}{3}\)
d, \(\left(\dfrac{1}{2}-1\right).\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{2017}-1\right)\)
e,\(\left(\dfrac{2}{3}\right):\left(\dfrac{4}{9}\right)^{10}\)
f,\(\left(\dfrac{1}{7}\right)^7.7^7\)
g, \(\dfrac{\left(125\right)^5}{5^{15}}\)
2 tìm x, biết
a, \(\dfrac{-4}{7}-x=\dfrac{5}{7}\)
b, \(x:\left(\dfrac{-3}{8}\right)=\dfrac{1}{2}\)
c, \(\dfrac{-3}{5}+\dfrac{1}{4}:x=\dfrac{-2}{5}\)
d, \(\left(x-\dfrac{2}{5}\right).\left(x+\dfrac{3}{7}\right)=0\)
e, \(\left(x+1\right)^5=-32\)
f, \(x-\left(1,5-7\right)=0,35\)
3 tìm số tự nhiên n biết
a, \(3^n=81\)
b, \(2^n=16\)
c, \(2.2^n=16\)
d, \(2.8^n=128\)
5 so sánh
a, \(2^{333}\) và \(3^{222}\)
b, \(\left(\dfrac{-1}{16}\right)^{100}\) và \(\left(\dfrac{-1}{2}\right)^{400}\)
Bài 1: Thực hiện phép tính:
\(A=\left(-\dfrac{1}{125}\right)^{11}:\left(\dfrac{1}{5}\right)^{32}\)
\(B=1+\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2+....+\left(\dfrac{1}{3}\right)^{2018}\)
\(C=\dfrac{16^3\cdot3^{10}+120\cdot6^9}{4^6\cdot3^{12}+6^{11}}\)
\(D=\left(\dfrac{0.4-\dfrac{2}{9}+\dfrac{2}{11}}{1.4-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{1}{3}-0.25+\dfrac{1}{5}}{1\dfrac{1}{6}-0.875+0.7}\right):\dfrac{2017}{2018}\)
\(E=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\)
\(G=\dfrac{\left(\dfrac{2}{5}\right)^7\cdot5^7+\left(2\dfrac{1}{4}\right)^3:\left(\dfrac{3}{16}\right)^3}{512+2^7\cdot5^2}:\dfrac{\left(\dfrac{1}{2}\right)^0}{\left(-1\right)^{2017}}\)
Mn ơi giúp e với ........ Em đang cần gấp giúp e với nha!!
Thank you mn nhiều nhiều.....
Cho biểu thức
A = \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+..........+\dfrac{1}{2019}\)
B = \(\dfrac{2018}{1}+\dfrac{2017}{2}+\dfrac{2016}{3}+.......+\dfrac{1}{2018}\) Chứng tỏ rằng \(\dfrac{B}{A}\)là số nguyên
Cho \(A=\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)\left(\dfrac{1}{4^2}-1\right)...\left(\dfrac{1}{100^2}-1\right)\) thì \(A< \dfrac{1}{2}\)
thực hiện các phép tính
a) \(-1\dfrac{1}{2}.21\dfrac{1}{3}+1\dfrac{1}{2}.1\dfrac{1}{3}\)
b) \(\dfrac{2018}{2019}.\left(13-13\dfrac{2018}{2019}\right)-\dfrac{1}{2019}:\dfrac{2019}{2018}\)
