\(2^{-1}.2^n+2^n=5.2^n\\ \Leftrightarrow\dfrac{1}{2}.2^n+2^n-5.2^n=0\\ \Leftrightarrow2^n\left(\dfrac{1}{2}+1-5\right)=0\\ \Leftrightarrow-\dfrac{7}{2}.2^n=0\\ \Leftrightarrow2^n=0\\ \Leftrightarrow n\in\varnothing\)
Tìm \(n\in\) N*, biết: \(2n\div\left(1+\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+...+\dfrac{1}{1+2+3+4+...+n}\right)=2020\)
\(\dfrac{\left(\dfrac{-5}{7}\right)^n}{\left(\dfrac{-5}{7}\right)^{n-1}}\left(n\ge1\right)\) Tính
b) \(\dfrac{\left(-\dfrac{1}{2}\right)^{2n}}{\left(-\dfrac{1}{2}\right)^n}\left(n\in N\right)\)
Bài 1: Tìm n \(\in\) Z biết:
\(e)3^{-1}.3^n+6.3^{n-1}=7.3^6\)
\(g)3^4< \dfrac{1}{9}.27^n< 3^{10}\)
\(h)25< 5^n:5< 625\)
Bài 2: Tìm x biết:
\(\dfrac{2.\left(\dfrac{-1}{2}\right).\left(\dfrac{2}{3}\right)^2-3.\left(\dfrac{-1}{2}\right)^2.\dfrac{2}{3}+1}{3.\left(\dfrac{-1}{2}\right)-\dfrac{2}{3}}\)
Help me !!!!!!!!!!!!! giúp mk vs các bn giỏi toán 
a)1/9. 27n =3n
b)2-1. 2n + 4.2n= 9.2n
c) a(n-2)(n-3)=1
2) tìm số tự nhiên n biết:
\(\left(\dfrac{1}{3}\right)^n=\dfrac{1}{27};\left(\dfrac{3}{5}\right)^n=\dfrac{81}{625}\)
cho Sn=\(\frac{1^2-1}{1}+\frac{2^2-1}{2^2}+\frac{3^3-1}{3^3}+...+\frac{n^2-1}{n^2}\)
CMR Sn không phải là số nguyên
A= 3^n+3+ 2^n+3+3^n+1+2^n+2 CMR A:6
Chứng minh với mọi n thuộc Z, n>0 thì:
3^n+3 +3^n+1 +2^n+3 +2^n+2 chia hết cho 6
tim so tu nhien n thoa man 2x2^2 + 3x2^3+ 4x2^4+...+(n-1)x2^n-1 +nx2^n=2^n+34
