đặt \(A=1+2+2^2+2^3+...............+2^{2016}\)
\(2A=2+2^2+2^3+2^4+....................+2^{2017}\)
\(2A-A=\left(2+2^2+2^3+...+2^{2017}\right)-\left(1+2+2^2+2^3+...+2016\right)\)
\(A=2^{2017}-1\)
thay vào S, ta được:
\(S=\dfrac{2^{2017}-1}{1-2^{2017}}=-1\)
Cho \(T=\dfrac{2}{2^1}+\dfrac{3}{2^2}+\dfrac{4}{2^3}+...+\dfrac{2017}{2^{2016}}+\dfrac{2018}{2^{2017}}\) . So sánh T và 3
\(A=\dfrac{2016^2+1^2}{2016\cdot1}+\dfrac{2015^2+2^2}{2015\cdot1}+\dfrac{2014^2+3^2}{2014\cdot3}+...+\dfrac{1009^2+1008^2}{1009\cdot1008}\)
và \(B=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2017}\)Tìm A/B
Cho A = ( \(\dfrac{1}{2^2}-1\) ) ( \(\dfrac{1}{3^2}-1\) ) ( \(\dfrac{1}{4^2}-1\)) ..... ( \(\dfrac{1}{2016^2}-1\) ) ( \(\dfrac{1}{2017^2}-1\) ) và B = \(-\dfrac{1}{2}\) . Hãy so sánh A và B
\(\dfrac{X-1}{2019}+\dfrac{X-2}{2018}=\dfrac{X-3}{2017}+\dfrac{X-4}{2016}\)
so sanh A va B
A=2017^100 / 1+2017+2017^2+2017^3+...+2017^100
B=2016^100 / 1+2016+2016^2+2016^3+...+2016^100
a) Tính A = ( 1 - \(\dfrac{1}{2}\) )( 1 - \(\dfrac{1}{3}\) ) (1-\(\dfrac{1}{4}\) ) ....(1-\(\dfrac{1}{2014}\) ) (1-\(\dfrac{1}{2015}\) ) (1-\(\dfrac{1}{2016}\) )
b)Tìm x biết \(\dfrac{x-2}{12}\) + \(\dfrac{x-2}{20}\) + \(\dfrac{x-2}{30}\)+ \(\dfrac{x-2}{42}\) + \(\dfrac{x-2}{56}\) +\(\dfrac{x-2}{72}\) = \(\dfrac{16}{9}\)
8.Find the value of 1+2+3+4+5+...+2016+2017+2016+2015+...+3+2+1.
B = \(\dfrac{1}{2^2}+\dfrac{1}{2^3}+.......+\dfrac{1}{2^{2017}}+\dfrac{1}{2^{2018}}\)
tính B
\(\dfrac{1}{4}+\dfrac{2}{4^2}+\dfrac{3}{4^3}+...+\dfrac{2017}{4^{2017}}\)
Chứng minh rằng :
\(A< \dfrac{1}{2}\)
