a)\(\frac{1}{3^2}\cdot3^{3n}=3^n\Rightarrow3=3^{3n-2}=3^n\Rightarrow3n-2=n\Rightarrow n=1\)
b)\(\frac{1}{3^2}\cdot3^4\cdot3^n=3^7\Rightarrow3^{n+2}=3^7\Rightarrow n+2=7\Rightarrow n=5\)
RÚT GỌN
a/\(\frac{9^4\cdot27^5\cdot3^6\cdot3^4}{3^8\cdot81^4\cdot234\cdot8^6}\)
b/\(N=\frac{4^6\cdot9^5+6^6\cdot120}{8^4-3^{12}-6}\)
Tính \(A=\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{44\cdot49}\right)\cdot\frac{1-3-5-7-...-49}{89}\)
\(B=\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^{10}\cdot6^{19}-7\cdot2^{29}\cdot27^6}-\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
Bài 1:
a) \(\frac{1}{1}\cdot2+\frac{1}{2}\cdot3+\frac{1}{3}\cdot4+...+\frac{1}{n}\cdot\left(n+1\right)\)
b) \(\frac{1}{1}\cdot2\cdot3+\frac{1}{2}\cdot3\cdot4+\frac{1}{3}\cdot4\cdot5+...+\frac{1}{a}\cdot\left(a+1\right)\cdot\left(a+2\right)\)
1 Tìm x,y
1) \(\frac{1+3y}{12}=\frac{1+5y}{5x}=\frac{1+7y}{4x}\)
2 tìm giá trị nhỏ nhất hoac lớn nhat cua các biểu thức sau
A=\(\frac{x^2+5}{x^2+3}\)
3 chứng minh rằng: Với mọi số nguyên dương n thì :
\(3^{n+2}-2^{n+2}+3^n-2^n\)chia hết cho 10
4 tính
\(\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+....+\frac{1}{44\cdot49}\right)\frac{1-3-5-7-...-49}{89}\)
A=\(\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
5 Tìm x biết
a) \(_{\left(x-7\right)^{x+1}-\left(x-7\right)^{x-11}=0}\)
b) \(\frac{1}{8}\cdot16^x=2^x\)
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,\(\left(\frac{1}{3}\right)^2\cdot\frac{1}{3}\cdot9^2\)
Viết các biểu thức sau dưới dạng an (a thuộc Q, n thuộc 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)\(\left(\frac{1}{3}\right)^2\cdot\frac{1}{3}\cdot9^2\)
giúp mk giải đầy đủ nhé!
Tính \(\frac{B}{A}\)biết
\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+....+\frac{1}{n\left(n+1\right)}+...+\frac{1}{2008\cdot2009}\)
\(B=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}+...+\frac{1}{2008\cdot2009\cdot2010}\)
cho Sn= \(\frac{1}{1\cdot2\cdot3\cdot4}\)+ \(\frac{1}{2\cdot3\cdot4\cdot5}\)+ ... + \(\frac{1}{n\cdot\left(n+1\right)\cdot\left(n+2\right)\cdot\left(n+3\right)}\)
CMR: 18<\(\frac{1}{S_n}\)<=24
\(B=\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\frac{56^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)