1. Tìm số tự nhiên n sao cho :
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+..+\dfrac{1}{n.\left(n+1\right)}=\dfrac{2999}{3000}\)
2. Tính :
a ) \(S=2018.3+2018.4+2018.5+...+2018.2018\)
b ) \(\dfrac{1}{\sqrt{8}+\sqrt{10}}+\dfrac{1}{\sqrt{10}+\sqrt{12}}+\dfrac{1}{\sqrt{12}+\sqrt{14}}+...+\dfrac{1}{\sqrt{200}+\sqrt{202}}\)
c ) \(S=5.21^2+5.21^3+5.21^4+....+5.21^{2018}\)
d ) \(A=9+99+999+9999+...+9..9\)( 99 chữ số 9)
e ) 72+772+7772+...+77...72( 77 chữ số 7 )
2. Tính tổng :
a ) \(S=\dfrac{1}{3\sqrt{1}+3\sqrt{3}}+\dfrac{1}{3\sqrt{3}+3\sqrt{5}}+...+\dfrac{1}{3\sqrt{2017}+3\sqrt{2019}}\)
b ) S = \(\dfrac{1}{\sqrt{2.2}+\sqrt{2.3}}+\dfrac{1}{\sqrt{2.3}+\sqrt{2.4}}+\dfrac{1}{\sqrt{2.4}+\sqrt{2.5}}+...+\dfrac{1}{\sqrt{2.2018}+\sqrt{2.2019}}\)
Tính:
A=(1/1009+1/1010+...+1/2016+1/2017):(1-1/2+1/3-1/4+...+1/2018-1/2016+1/2017)
a) Tìm x(x thuộc N*), biết \(\left(1+\dfrac{1}{1.3}\right)\left(1+\dfrac{1}{2.4}\right)\left(1+\dfrac{1}{3.5}\right)...\left(1+\dfrac{1}{x\left(x+2\right)}\right)=\dfrac{31}{16}\)
b) Chứng tỏ \(\dfrac{2}{2^2}+\dfrac{2}{4^2}+\dfrac{2}{6^2}+...+\dfrac{2}{2016^2}< \dfrac{2016}{2017}\)
c) Chứng tỏ \(\dfrac{1}{5^2}+\dfrac{1}{9^2}+\dfrac{1}{13^2}+...+\dfrac{1}{41^2}< \dfrac{10}{129}\)
CMR: N=2016^3-2016 ⋮ 2015; ⋮ 2017
Tìm x biết\(\frac{x-1}{2017}\)+\(\frac{x-2}{2016}\)+\(\frac{x-3}{2015}\)+....+\(\frac{x-2017}{1}\)=2017
Tìm x biết \(\frac{x-1}{2017}\)+\(\frac{x-2}{2016}\)+\(\frac{x-3}{2015}\)+....+\(\frac{x+2017}{1}\)=2017
\(\frac{x-3}{2016}+1=\frac{x-2}{2017}+\frac{x-1}{2018}\)
\(\dfrac{x+1}{2015}+\dfrac{x+2}{2016}=\dfrac{x+3}{2017}+\dfrac{x+4}{2018}\)
giải bài này gấp
cho f(x)=x^3-3x^2+3x+3 cm f(2018/2017)< f(2017/2016)
