tính nhanh :
\(A=\frac{15^3+5\times15^2-5^3}{18^3+6\times18^2-6^3}\)
\(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^{2015}}\)
\(C=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{16}\left(1+2+...+16\right)\) \(D=\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\)
\(F=\left(100-1^2\right)\left(100-2^2\right)....\left(100-25^2\right)\)
Rút gọn:
a) \(C=\frac{\left(\frac{2}{3}\right)^3\times\left(-\frac{3}{4}\right)^2\times\left(-1\right)^5}{\left(\frac{2}{5}\right)^2\times\left(-\frac{5}{12}\right)^2}\) b) \(D=\frac{6^6+6^3\times3^3+3^6}{-73}\)
TÍNH
\(\frac{\left(1+2+3+...+100\right)\times\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right)\times\left(6,3\times12-21\times3,6\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
\(4\times\left(\frac{1}{4}\right)^2+25\times\left[\left(\frac{3}{4}\right)^3\div\left(\frac{5}{4}\right)^3\right]\div\left(\frac{3}{2}\right)^3\)
\(2^3+3\times\left(\frac{1}{2}\right)^0-1+\left[\left(-2\right)^2\div\frac{1}{2}\right]-8\)
1. Rút gọn a. \(B=\frac{\left(-\frac{1}{3}\right)^3-\left(\frac{3}{4}\right)^3\times\left(-2\right)^2}{2\times\left(-1\right)^5+\left(\frac{3}{2}\right)^2-\frac{3}{8}}\) b.\(C=\frac{\left(\frac{1}{2}\right)^3\times2^{-2}\times8}{\left(-23\right)^2\times16}\)
BÀi 1: Thực hiện phép tính ( tính nhanh nếu có thể)
a.\(\left(-\frac{1}{2}\right)-\left(-\frac{3}{5}\right)+\left(-\frac{1}{9}\right)+\frac{1}{71}-\left(-\frac{2}{7}\right)+\frac{4}{35}-\frac{7}{18}\)
b.\(\left(3-\frac{1}{4}+\frac{2}{3}\right)-\left(5-\frac{1}{3}-\frac{6}{5}\right)-\left(6-\frac{7}{4}+\frac{3}{2}\right)\)
c.\(\frac{3}{5}:\left(\frac{-1}{15}-\frac{1}{6}\right)+\frac{3}{5}:\left(\frac{1}{3}-1\frac{1}{15}\right)\)
\(4\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{6}\right)\le x\le-\frac{2}{3}\times\left(\frac{1}{3}-\frac{1}{2}-\frac{3}{4}\right)\)
BT: Rút gọn: \(A=\frac{\left(1+2+3+...+99+100\right)\times\left(\frac{1}{4}+\frac{1}{6}-\frac{1}{2}\right)\times\left(63\times1,2-21\times3,6+1\right)}{1-2+3-4+5-6+...+99-100}\)
Giúp mình với!!! Tối mai mình học rồi!!! Cảm ơn các bạn nhiều!!!
tính \(A=\frac{1}{2}\times\left(1+\frac{1}{1\times3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times...\times\left(1+\frac{1}{2015\times2017}\right)\)