tìm số tự nhiên thỏa mãn điều kiện
\(2\cdot2^2+3\cdot2^3+4\cdot2^4+........+n\cdot2^n=2^{n+11}\)
rút gọn : \(A=\left(\dfrac{2}{5}-\dfrac{5}{2}+\dfrac{1}{10}\right):\left(\dfrac{5}{2}-\dfrac{2}{3}+\dfrac{1}{12}\right)\)
tính:\(B=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+......+\dfrac{1}{2017}}{\dfrac{2016}{1}+\dfrac{2003}{2}+\dfrac{2002}{3}+.......+\dfrac{1}{2016}}\)
CMR :\(5a+2b⋮13\Leftrightarrow9a+b⋮13\left(a,b\in Z\right)\)
A=\(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{44.49}+\left(\dfrac{1-3-5-7-...-49}{89}\right)\)
B=\(\dfrac{212.3^5.4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^4.49^2}{\left(125.71^3+59.14^3\right)}\)
C=\(\dfrac{\dfrac{1}{2003}+\dfrac{1}{2004}-\dfrac{1}{2005}}{\dfrac{5}{2003}+\dfrac{5}{2004}-\dfrac{5}{2005}}-\dfrac{\dfrac{2}{2002}+\dfrac{2}{2003}-\dfrac{2}{2004}}{\dfrac{3}{2002}+\dfrac{3}{2003}-\dfrac{3}{2004}}\)
D=\(\left(\dfrac{1,5+1-0,75}{2,5+\dfrac{5}{3}-1,25}\right)+\left(\dfrac{0,375-0,3+\dfrac{3}{11}+\dfrac{3}{12}}{-0,625+0,5-\dfrac{5}{11}-\dfrac{5}{12}}\right):\dfrac{1890}{2005}+115\)
E=13+23+...+103=3025
Tính F=23+42+63+...+203=?
a,\(\dfrac{8^{20}+4^{20}}{4^{25}+64^5}\)
b,\(\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right).\left(\dfrac{4}{5}-\dfrac{3}{4}\right)^2\)
c,\(23\dfrac{1}{3}:\left(\dfrac{-5}{7}\right)-13\dfrac{1}{3}:\left(\dfrac{-5}{7}\right)\)
d,1:\(\left(\dfrac{2}{3}-\dfrac{3}{4}\right)^2\)
e,\(\dfrac{45^{10}.5^{20}}{75^{15}}\)
Tính giá trị biểu thức:
a,\(A=\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
b,\(^{B=\dfrac{\left[\left(6,2:0,31-\dfrac{5}{6}.0,9\right).0,2+0,15\right]:12}{\left(2+1\dfrac{4}{11}.0,22:0,1\right).\dfrac{1}{33}}}\)
c,\(C=\dfrac{\left(\dfrac{3}{4}\right)^3+\left(\dfrac{5}{4}\right)^3-5\left(\dfrac{4}{3}-\dfrac{5}{4}\right)}{\left(\dfrac{-5}{8}\right)^2+\left(\dfrac{2}{3}\right)^2-\dfrac{5}{6}}\)
d,\(D=\left[\dfrac{\dfrac{17}{24}.9\dfrac{1}{2}-3\dfrac{1}{4}.\dfrac{17}{24}}{3\dfrac{1}{2}.2\dfrac{13}{36}+2\dfrac{13}{36}.2\dfrac{3}{4}}-\dfrac{1}{5}\right]^{-2}\)
Giúp em với chị @Nhã Doanh ới!!!!!!!!
Mai em phải đi thi rồi :((
Tính tổng đại số
\(A=\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}-\dfrac{1}{5}-\dfrac{2}{5}-\dfrac{3}{5}-\dfrac{4}{5}+...+\dfrac{1}{10}+\dfrac{2}{10}+...+\dfrac{9}{10}\)
\(B=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}+...+\dfrac{1}{n}+\dfrac{2}{n}+...+\dfrac{n-1}{n}\)\(\left(n\in Z,n\ge2\right)\)
Tinh:
\(A=\dfrac{(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}).203\dfrac{1}{25}+46\dfrac{3}{4}}{(1\dfrac{3}{7}+\dfrac{10}{3}):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
\(B=\dfrac{\left(81,624:4,8-4.505\right)^2+125.0,75}{\left\{\left[\left(0,44\right)^2:0,88+3,53\right]^2-\left(2,75\right)^2\right\}:0,52}\)
\(\dfrac{\left(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}\right).230\dfrac{1}{25}+46\dfrac{3}{4}}{\left(1\dfrac{3}{10}+\dfrac{10}{3}\right):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
\(\dfrac{\left(1+2+3+...+99+100\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+.....+99-100}\)
có ai giúp mình được không :
a) \(\dfrac{1}{4}-\dfrac{3}{4}:\left(\dfrac{-5}{8}\right)\)
b) \(3-\left(\dfrac{-6}{7}\right)^0+\sqrt{\dfrac{1}{16}}:2\)
c) \(\dfrac{9^5\cdot2^6}{4^3\cdot3^8}\)
Thực hiên phép tính
\(\dfrac{\left(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}\right).230\dfrac{1}{25}+46\dfrac{3}{4}}{\left(1\dfrac{3}{7}+\dfrac{10}{3}\right):\left(12\dfrac{1}{3}\right)-14\dfrac{2}{7}}\)
giúp mình với
gấp gấp lắm
1/ tìm x
a) \(x.\left(x+\dfrac{2}{3}\right)=0\)
2/tìm giá trị nhỏ nhất của các biểu thức
a) \(\left|x+\dfrac{4}{6}\right|\)
b) \(\left|x-\dfrac{1}{3}\right|\)
3/ tính
a) \(\left(1+2+3+...90\right).\left(12.34-668\right):\left(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}\right)\)
b) \(\dfrac{\dfrac{3}{7}-\dfrac{3}{11}+\dfrac{3}{13}}{\dfrac{5}{7}-\dfrac{5}{11}+\dfrac{5}{13}}+\dfrac{\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}}{\dfrac{5}{4}-\dfrac{5}{6}+\dfrac{5}{8}}\)