bài 1: tính nhanh
a, (100-13).(100-23).(100-33)..........(100-503)
b, \(\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}+...........+\frac{5^2}{56.61}\)
c, \(2^{100}-2^{99}+2^{98}-2^{97}+.......+2^2-2^1\)
d, \(2015^{\left(1.4.9.6\right).\left(1.4.9.7\right).\left(1.4.9.8\right)....\left(1.9.9.9\right)}\)
bài 2: Tính
a, \(A=\left(-1\right).\left(-1\right)^2.\left(-1\right)^3.\left(-1\right)^4.\left(-1\right)^5.........\left(-1\right)^{99}\)
b, \(B=512-\frac{512}{2}-\frac{512}{2^2}-\frac{512}{2^3}-........-\frac{512}{2^{10}}\)
thực hiên các phép tính tính :
a) \(\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right).\frac{5}{19}}{\left(\frac{1}{14}+\frac{1}{7}-\frac{-3}{35}\right).\frac{-4}{3}}\)
b) \(\frac{\left(1+2+3+...+100\right).\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(6,3.12-21.3,6\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
Tính \(A=\frac{\left(1+2+3+...+100\right)\cdot\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{4}-\frac{1}{5}\right)\cdot\left(2,4\cdot42-21\cdot4,8\right)}{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}}\)
TÍNH
\(\frac{\left(1+2+3+...+100\right)\times\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right)\times\left(6,3\times12-21\times3,6\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
a, Tính : \(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
b, Tính : \(P=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}}{\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{1}{2011}}\)
c, Tính : \(\frac{\left(1+2+3+...+99+100\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{7}-\frac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+...+99-100}\)
Tính nhanh
\(\frac{\left(1+2+3+...+99+100\right).\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(6,3.12-21.3,6\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
tính nhanh :
\(A=\frac{15^3+5\times15^2-5^3}{18^3+6\times18^2-6^3}\)
\(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^{2015}}\)
\(C=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+...+16\right)\) \(D=\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\)
\(F=\left(100-1^2\right)\left(100-2^2\right)....\left(100-25^2\right)\)
1) Tính nhanh \(\frac{\left(1+2+3+...+100\right).\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.,..................+\frac{1}{100}}\)
Tính
a) \(\left(\frac{2}{5}\right)^5:\left(\frac{9}{25}\right)^5\)
\(b.25.5^3.\frac{1}{625}.5^2\)
c. \(\frac{20^5.5^{10}}{100^5}\)
\(\left(\frac{1}{7}\right)^2.\frac{1}{7}.49^2\)