Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a) \(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)
\(\Rightarrow2^n\cdot\left(2^{-1}+4\right)=9\cdot2^5\)
\(\Rightarrow2^n\cdot4,5=288\)
\(\Rightarrow2^n=64\)
\(\Rightarrow n=6\)
b) \(2^m-2^n=1984\)
\(\Rightarrow2^n\cdot\left(2^{m-n}-1\right)=2^6\cdot31\)
\(\Rightarrow\left\{{}\begin{matrix}2^n=2^6\\2^{m-n}-1=31\end{matrix}\right.\)
\(\Rightarrow n=6\)
\(\Rightarrow2^{m-n}=32\Rightarrow m-n=5\Rightarrow m=11\)
a) 81 = (-243)( - 3n)
33 = 35.3n
32.3n = 1
n =2 vì 32-2 = 3o = 1
b) 2n (1/2 +4) = 9.25
2n.9/2 = 9.25
2n = 26
n = 6
Bài 1:
\(A=1\cdot2+2\cdot3+...+n\left(n+1\right)\)
\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+n\left(n+1\right)\left[\left(n+2\right)-\left(n-1\right)\right]\)
\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+n\left(n+1\right)\left(n+2\right)-\left(n-1\right)n\left(n+1\right)\)
\(3A=n\left(n+1\right)\left(n+2\right)\Rightarrow A=\frac{n\left(n+1\right)\left(n+2\right)}{3}\)
Bài 2:
\(B=1^2+2^2+...+n^2\)
\(B=1\left(2-1\right)+2\left(3-1\right)+...+n\left[\left(n+1\right)-1\right]\)
\(B=\left[1\cdot2+2\cdot3+...+n\left(n+1\right)\right]-\left(1+2+...+n\right)\)
\(B=\frac{n\left(n+1\right)\left(n+2\right)}{3}-\frac{n\left(n+1\right)}{2}\)
\(B=\frac{n\left(n+1\right)\left(2n+1\right)}{6}\)
A=\(2.2^2+3.2^3+4.2^4+...+100.2^{100}\)
\(\Rightarrow2A=2.2^3+3.2^4+4.2^5+...+100.2^{101}\)
\(\Rightarrow A-2A=2.2^2+\left(3.2^3-2.2^3\right)+\left(4.2^4-3.2^4\right)+...+\left(100.2^{100}-99.2^{100}\right)-100.2^{101}\)
\(\Rightarrow-A=2^3+\left(2^3+2^4+...+2^{100}\right)-100.2^{101}\)
Đặt \(B=\left(2^3+2^4+...+2^{100}\right)\)
\(\Rightarrow2B=\left(2^4+2^5+...+2^{101}\right)\)
\(\Rightarrow2B-B=\left(2^4+2^5+...+2^{101}\right)-\left(2^3+2^4+...+2^{100}\right)\)
\(\Rightarrow B=2^{101}-2^3\)
\(\Rightarrow-A=2^3+2^{101}-2^3-100.2^{101}\)
\(\Rightarrow-A=2^{101}-100.2^{101}\)
\(\Rightarrow A=100.2^{101}-2^{101}=99.2^{101}\)
bạ̣̣̣̣n vao cau hoi tuong tu hoac len google