Tính nhanh
a)\(\frac{120-\left(-0,5\right).\left(-40\right).\left(-5\right).\left(-0,2\right).20.0,25}{5+10+15+...+1995}\)
b)\(\frac{5.18-10.27+15.36}{10.36-20.54+30.72}\)
c)\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)...\left(\frac{1}{1999}-1\right)\)
1 Tìm số dư khi chia A ,B cho 2 biết
A=\(\left(4^n+6^n+8^n+10^n\right)-\left(3^n+5^n+7^n+9^n\right)\left(n\in N\right)\)
B=\(1995^n+1996^n+1997^n\left(n\in N\right)\)
2.Tìm chữ số tận cùng của \(9^{9^{2000}}\)
b.tìm 3 chứ số tận cùng của \(2008^{100}\)
3.tìm (x,y)thõa mãn:\(\left(\frac{2x-5}{9}\right)^{2016}+\left(\frac{3y+0,4}{3}\right)^{2012}=0\)
b,\(x\left(x+y\right)=\frac{1}{48}\) và \(y\left(x+y\right)=\frac{1}{24}\)
tính G=\(\frac{\left(1+\frac{1015}{1}\right)\left(1+\frac{1015}{2}\right)\left(1+\frac{1015}{3}\right)...\left(1+\frac{1015}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)\left(1+\frac{1000}{3}\right)...\left(1+\frac{1000}{1015}\right)}\)
Tính bằng cách hợp lí nhất
a) A = \(\frac{\left(1+17\right)\left(1+\frac{17}{2}\right)\left(1+\frac{17}{3}\right)...\left(1+\frac{17}{19}\right)}{\left(1+19\right)\left(1+\frac{19}{2}\right)\left(1+\frac{19}{3}\right)..\left(1+\frac{19}{17}\right)}\)
b) B = \(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{99}-1\right)\left(\frac{1}{100}-1\right)\)
\(\frac{\left(1+17\right)+\left(1+\frac{17}{2}\right)+\left(1+\frac{17}{3}\right)+........+\left(1+\frac{17}{19}\right)}{\left(1+19\right)+\left(1+\frac{19}{2}\right)+\left(1+\frac{19}{3}\right)+........+\left(1+\frac{19}{17}\right)}\)
Tìm GTNN, GTLN:
\(C=\frac{1996x+1}{1997x-1997}\left(\cdot x+1\right)\)
\(F=\frac{2\left|x\right|+3}{3\left|x\right|-1}\)
\(K=\left|x-1\right|+\left|x-2\right|+\left|x-3\right|\)
\(M=\left|x-2\right|+\left|x+28\right|+\left|x-60\right|\)
\(\left[6\cdot\left(-\frac{1}{3}\right)^2-3\cdot\left(-\frac{1}{3}\right)+1\right]:\left(-\frac{1}{3}-1\right)\)
\(\frac{\left(\frac{2}{3}\right)^3\cdot\left(-\frac{3}{4}\right)^2\cdot\left(-1\right)^{2003}}{\left(\frac{2}{5}\right)^2\cdot\left(-\frac{5}{12}\right)^3}\)
\(A=\frac{\left(1+17\right)\left(1+\frac{17}{2}\right)\left(1+\frac{17}{3}\right)....\left(1+\frac{17}{19}\right)}{\left(1+19\right)\left(1+\frac{19}{2}\right)\left(1+\frac{19}{3}\right).....\left(1+\frac{19}{17}\right)}\)=?
Tính
\(\frac{\left(1+17\right).\left(1+\frac{17}{2}\right).\left(1+\frac{17}{3}\right)....\left(1+\frac{17}{19}\right)}{\left(1+19\right).\left(1+\frac{19}{2}\right).\left(1+\frac{19}{3}\right)....\left(1+\frac{19}{17}\right)}\)