Tìm chữ số tận cùng của: \(1+3+3^2+3^3+.......+3^{2014}\)
Giải: ta có: \(1+3+3^2+3^3+.......+3^{2014}\)
\(=1+\left(3+3^3\right)+\left(3^2+3^4\right)+\left(3^5+3^7\right)+....+\left(3^{2012}+3^{2014}\right)\)
\(=1+3\left(1+3^2\right)+3^2\left(1+3^2\right)+....+3^{2012}\left(1+3^2\right)\)
\(=1+\left(1+3^2\right)\left(3+3^2+3^5+.....+3^{2012}\right)\)
\(=1+10\left(3+3^2+3^5+...+3^{2012}\right)\)
\(=1+\overline{.......0}=\overline{.....1}\)
Vậy chữ số tận cùng của day trên là 1
BT1: Tính
1) \(\dfrac{1}{2011}+\dfrac{2012.2010}{2011}-2012\)
2) \(\left(2-\dfrac{2}{3}\right)\left(2-\dfrac{4}{3}\right)\left(2-\dfrac{5}{4}\right)\left(2-\dfrac{6}{5}\right)\)
Tính S=\(\left(1-\dfrac{1}{1+2}\right).\left(1-\dfrac{1}{1+2+3}\right).\left(1-\dfrac{1}{1+2+3+4}\right).....\left(1-\dfrac{1}{1+2+...+2014}\right)\)
1: rút gọn rồi tính
\(\left(-\dfrac{72}{40}-\dfrac{144}{60}-2\dfrac{1}{3}\right)\) : \(\left(\dfrac{45}{100}-\dfrac{25}{60}+-\dfrac{75}{25}\right)\)
2: tìm x: \(3\cdot\left(4-x\right)+\left(x+2\right)\cdot\left(1+2x\right)=7\cdot\left(1+x\right)-2x\cdot\left(2-x\right)\)
3: tìm x: \(\dfrac{2\cdot\left(1+x\right)}{3}-\dfrac{5\cdot\left(2-x\right)}{6}=1\dfrac{1}{3}-\dfrac{3\cdot\left(2x+3\right)}{4}-1\dfrac{1}{2}\cdot\left(x+1\right)\)
4: cho a= \(3+3^{2^3}+3^3+3^4+...+3^{360}\)
Tính giá trị biểu thức :
\(\dfrac{1}{2}-\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}\right)-\left(\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{4}{5}\right)+\left(\dfrac{1}{6}+\dfrac{2}{6}+\dfrac{3}{6}+\dfrac{4}{6}+\dfrac{5}{6}\right)-\left(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{4}{7}+\dfrac{5}{7}+\dfrac{6}{7}\right)+...+\left(100+...+\dfrac{99}{100}\right)\)
tính:
\(\dfrac{2}{5}x\dfrac{1}{3}-\dfrac{2}{15}:\dfrac{1}{5}+\dfrac{3}{5}x\dfrac{1}{3}\)
2)\(\left(3\dfrac{1}{3}+2,5\right):\left(3\dfrac{1}{6}-4\dfrac{1}{5}\right)-\dfrac{11}{31}\)
3)\(\left[6+\left(\dfrac{1}{2^{ }}\right)^3-\left|-\dfrac{1}{2}\right|\right]:\dfrac{3}{12}\)
4)\(\dfrac{18}{37}+\dfrac{8}{24}+\dfrac{19}{37}-1\dfrac{23}{24}+\dfrac{2}{3}\)
5) \(\left(-2\right)^3x\left(\dfrac{3}{4}-0,25\right):\left(2\dfrac{1}{4}-1\dfrac{1}{6}\right)\)
6)\(\left(\dfrac{2}{5}\right)^2+5\dfrac{1}{2}x\left(45-2\right)+\dfrac{23}{-4}\)
7)\(\dfrac{4}{9}-19\dfrac{1}{3}-\dfrac{4}{9}x39\dfrac{1}{3}\)
8)\(\left(-\dfrac{1}{2}\right)^2:\dfrac{1}{4}-2x\left(-\dfrac{1}{2}\right)^2\)
9)\(125\%x\left(-\dfrac{1}{2}\right)^3:\left(1\dfrac{5}{16}-1,5\right)+2008^0\)
giúp mình nha mai mình học rùi 
Tính
a) \(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).....\left(1-\dfrac{1}{2012}\right)\)
BT1: Tính
1) \(\dfrac{1}{2}-\text{|}\dfrac{1}{5}-\dfrac{1}{4}\text{|}+\left(-\dfrac{1}{3}\right)^2\)
2) \(\dfrac{1}{3}+\dfrac{4}{3}.\left(\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{-2}{3}\right)^2\)
Tính nhanh:
11) \(\dfrac{5}{7}\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{4}{7}\right)+\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{4}{7}\right):\dfrac{7}{5}\)
12)\(\dfrac{43}{5}\left(\dfrac{17}{3}-\dfrac{16}{9}+2\right)-\dfrac{43}{5}\left(\dfrac{17}{3}-\dfrac{16}{9}\right)\)
\(P=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+\dfrac{1}{4}\left(1+2+3+4\right)+..+\dfrac{1}{2016}\left(1+2+..+2016\right)\)
tính giá trị P
