\(u_1=\dfrac{1}{\sqrt{2}};q=\dfrac{1}{\sqrt{2}}\)
\(S_{99}=\dfrac{\dfrac{1}{\sqrt{2}}\cdot\left(\dfrac{1}{\sqrt{2}}^{99}-1\right)}{\dfrac{1}{\sqrt{2}}-1}=\dfrac{1}{\sqrt{2}}\cdot\left(\dfrac{1-2^{49}\cdot\sqrt{2}}{2^{49}\cdot\sqrt{2}}\right):\dfrac{1-\sqrt{2}}{\sqrt{2}}\)
\(=\dfrac{1}{1-\sqrt{2}}\cdot\dfrac{1-2^{49}\cdot\sqrt{2}}{2^{49}\cdot\sqrt{2}}\)
giúp mình với
1, tính
a, \(7\times\sqrt{\dfrac{6^2}{7^2}}-\sqrt{25}+\sqrt{\dfrac{\left(-3\right)^2}{2}}\)
b, \(-\sqrt{\dfrac{64}{49}}-\dfrac{3}{5}\times\sqrt{\dfrac{25}{64}}+\sqrt{0,25}\)
c, \(\sqrt{\dfrac{10000}{5}}-\dfrac{1}{4}.\sqrt{\dfrac{16}{9}}+\sqrt{\dfrac{\left(-3\right)^2}{\left(4\right)}}\)
d, \(\left|\dfrac{1}{4}-\sqrt{0,0144}\right|-\dfrac{3}{2}+\sqrt{\dfrac{81}{169}}\)
\(\sqrt{16}.\left(-\dfrac{1}{2}\right)^3+3.\left(\dfrac{1}{2}\right)^2+2.\sqrt{\dfrac{1}{4}}\)
Tính:
a) \(\sqrt{\dfrac{9}{16}}-\dfrac{5}{6}+\dfrac{3}{2}\) b) \(\left(\dfrac{1}{9}+\dfrac{2}{3}\right)^2-\dfrac{5}{3}:\sqrt{25}\)
c)\(\dfrac{5}{11}.\left(-\dfrac{3}{7}\right)+\dfrac{5}{11}.\left(\dfrac{-5}{7}\right)+\left(-\dfrac{8}{7}\right).\dfrac{6}{11}\)
d) \(\dfrac{2^8.2^{18}}{8^5.4^6}\)
Thực hiện phép tính:
\(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(B=\dfrac{1-\dfrac{1}{\sqrt{49}}+\dfrac{1}{49}-\dfrac{1}{\left(7\sqrt{7}\right)^2}}{\dfrac{\sqrt{64}}{2}-\dfrac{4}{7}+\dfrac{2^2}{7^2}-\dfrac{4}{343}}\)
tính
A) \(5\sqrt{0,36}-10\sqrt{0,04}\)
b) \(\left(1+\dfrac{2}{3}-\dfrac{14}{9}\right):\left(\dfrac{5}{6}-\dfrac{4}{5}\right)^2\)
\(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\)
\(\left(\dfrac{15}{4}-5x\right)\cdot\left(9x^2-4\right)=0\)
\(\sqrt{x-2}+\dfrac{1}{3}=1\)
a) \(\sqrt{\left(-7\right)^2}+\sqrt{\dfrac{25}{16}}-\dfrac{3}{2}\) b) \(23\dfrac{1}{3}.\dfrac{-1}{4}-13\dfrac{1}{3}.\dfrac{-1}{4}\)
Rút gọn:
\(A=\left(1+\dfrac{\sqrt{x}}{x+1}\right):\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\sqrt{x}+\sqrt{x}-x-1}\right)-1\)
1) tính
a)\(9^{14}:\left(3^{12}.27^6\right)\)
B)\(\sqrt{\dfrac{4}{9}}+\left(\dfrac{-1}{2}\right)^3-|\dfrac{-2}{3}|\)
