b, \(A=3+3^2+3^3+....+3^{2016}\)

\(3A=3(3+3^2+3^3+...+3^{2016})\)

\(3A=3^2+3^3+3^4+...+3^{2016}+3^{2017}\)

\(2A=3A-A=(3^2+3^3+...+3^{2016}+3^{2017})-(3+3^2+3^3+...+3^{2016})\)\(2A=3^{2017}-3^{ }\)

\(\Rightarrow2A+3=3^{2017}-3+3\)

\(\Rightarrow2A+3=3^{2017}\)

\(\Rightarrow2x=2017\)

\(\Rightarrow2x=1008,5\)

Mà \(x\in Z\) nên suy ra \(x\in\varnothing\)

a,Ta có: A có 2016 số số hạng, ghép A thành 504 nhóm, mỗi nhóm có 4 số hạng như sau :

\(A=(3+3^2+3^3+3^4)+(3^5+3^6+3^7+3^8)+....+(3^{2013}+3^{2014}+3^{2015}+3^{2016})\)

\(A=3.(1+3+3^2)+3^5.(1+3+3^2)+....+3^{2013}.(1+3+3^2)\)

\(A=3.13+3^5.13+....+3^{2013}.13\)

\(A=13.(3+3^5+...+3^{2013})⋮13\)

\(\Rightarrow A⋮13\)

Chăm Học copy nhanh như tia chớp

Ggggggggggggggggggoooooooooooooooooooooooooooooooooooooooooodddddddddddddddddddddddddbbbbbbbbbbbbbbbbyyyyyyyyyyyeeeeeeeeeeee bạn Lê Minh Hằng

Để B \(\in\) Z \(\Rightarrow5⋮n-3\)

\(\Rightarrow n-3\inƯ\left(5\right)\)

\(\Rightarrow n-3\in\left\{\pm1;\pm3\right\}\)

\(\Rightarrow n\in\left\{0;2;3;6\right\}\)

E = \(\dfrac{1}{10.9}-\dfrac{1}{9.8}-\dfrac{1}{8.7}-\dfrac{1}{7.6}-\dfrac{1}{6.5}-\dfrac{1}{5.4}-\dfrac{1}{4.3}-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

E=\(\dfrac{1}{10}-\dfrac{1}{9}-\dfrac{1}{9}-\dfrac{1}{8}-\dfrac{1}{8}-\dfrac{1}{7}-\dfrac{1}{7}-\dfrac{1}{6}-\dfrac{1}{6}-\dfrac{1}{5}-\dfrac{1}{5}-\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{1}\)

E = \(\dfrac{1}{10}-\dfrac{1}{3}\)

E = \(\dfrac{-7}{30}\)