TÌM SỐ NGUYÊN n SAO CHO:
\(\frac{2^n}{2}\)+\(^{2^2\cdot2^n=9\cdot2^5}\)
Những câu hỏi liên quan
tìm số nguyên x
a)\(27^n:3^n=9\)
b)\(\left(\frac{-1}{3}\right)^N=\frac{1}{81}\)c)\(\frac{25}{5^n}=5\)d)\(\frac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\)e)\(\frac{81}{\left(-3\right)^n}=-243\)
Bn nào giải đc câu nào thì giải nhé ko giải đc câu nào thì thôi
Tìm số ngyên n biết \(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)
\(\Leftrightarrow2^n.\left(2^{-1}+4\right)=9.2^5\)
\(\Leftrightarrow2^n.4,5=4,5.2^6\)
\(\Rightarrow2^n=2^6\)
\(\Rightarrow n=6\)
Đúng 0
Bình luận (0)
CÂU 5:
Tìm số tự nhiên n thoả mãn: \(2\cdot2^2+3\cdot2^3+4\cdot2^4+.....+n\cdot2^n=2^{n+5}\)
MÌNH TICK CHO
Tìm số tự nhiên n thỏa mãn \(2\cdot2^2+3\cdot2^3+...n\cdot2^n=2^{n+5}\)
Đặt \(A=2.2^2+3.2^3+...+n.2^n\)
\(\Rightarrow2A=2.2^3+3.2^4+...+n.2^{n+1}\)
\(\Rightarrow A-2A=\)\(2.2^2+3.2^3+...+n.2^n\)\(-2.2^3-3.2^4-...-n.2^{n+1}\)
\(\Rightarrow-A=2.2^2+2^3+2^4+...+2^n-n.2^{n+1}\)
\(\Rightarrow-A=2^2+\left(2^2+2^3+2^4+...+2^{n+1}\right)-\left(n+1\right).2^{n+1}\)
\(\Rightarrow A=-2^2-\left(2^2+2^3+2^4+...+2^{n+1}\right)+\left(n+1\right).2^{n+1}\)
Đặt \(K=\left(2^2+2^3+2^4+...+2^{n+1}\right)\)
\(2K=\left(2^3+2^4+2^5+...+2^{n+2}\right)\)
\(2K-K=\left(2^3+2^4+2^5+...+2^{n+2}\right)\)\(-\left(2^2+2^3+2^4+...+2^{n+1}\right)\)
\(K=2^{n+2}-2^2\)
\(\Rightarrow A=-2^2-2^{n+2}+2^2+\left(n+1\right).2^{n+1}\)
\(\Rightarrow A=\left(n+1\right).2^{n+1}-2^{n+2}\)
\(\Rightarrow A=2^{n+1}\left(n+1-2\right)\)
\(\Rightarrow A=2^{n+1}\left(n-1\right)=2^{n+5}\Rightarrow2^4=n-1\Rightarrow n=17\)
Tìm n∈Z, biết :
a) \(\frac{1}{9}\cdot27^n=3^n\)
b) \(3^{-2}\cdot3^4\cdot3^n=3^7\)
c) \(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)
d) \(32^{-n}\cdot16^n=2048\)
Tìm \(n\in N\)
\(2\cdot2^2+3\cdot2^3+4\cdot2^4+...+\left(n-1\right)\cdot2^{n-1}+n\cdot2^n=2^{n+34}\)
N=\(\frac{5\cdot\left(2^2\cdot3^2\right)\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}\cdot3^6}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot2^{18}}\)
Tinh N
tìm n :\(2\cdot2^2+3.2^3+4\cdot2^4+.....+n\cdot2^n=2^{n+10}\)
Viết các biểu thức số sau dưới dạng an(a\(\in\)Q,n\(\in\)N)
a,\(9\cdot3^3\cdot\frac{1}{81}\cdot3^2\)
b,\(4\cdot2^5:\left(2^3\cdot\frac{1}{16}\right)\)
c,\(3^2\cdot2^5\cdot\left(\frac{2}{3}\right)^2\)
d,\(\left(\frac{1}{3}\right)^2\cdot\frac{1}{3}\cdot9^2\)