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\(\left\{\left[3^{14}.69+12.3^{14}\right]:3^{16}-7\right\}:2^4\)
\(=\left\{\left[3^{14}.\left(69+12\right)\right]:3^{16}-7\right\}:16\)
\(=\left\{\left[3^{14}.81\right]:3^{16}-7\right\}:16\)
\(=\left\{\left[3^{14}.3^4\right]:3^{16}-7\right\}:16\)
\(=\left\{3^{18}:3^{16}-7\right\}:16\)
\(=\left\{3^2-7\right\}:16\)
\(=\left\{9-7\right\}:16\)
\(=2:16\)
\(=\frac{1}{8}\)
\(=\frac{\left(2^{17}+5^{17}\right)\left(3^{14}-5^{12}\right)\left(16-16\right)}{15^2+5^3+67^7}=\frac{\left(2^{17}+5^{17}\right)\left(3^{14}-5^{12}\right).0}{15^2+5^3+67^7}=0\)
\(B=\left(\dfrac{-4}{5}+\dfrac{3}{3}\right)+\left(\dfrac{-5}{4}+\dfrac{14}{5}\right)+\left(\dfrac{7}{3}-2\right)\\ B=\left(\dfrac{-4}{5}+\dfrac{14}{5}\right)+\left(\dfrac{3}{3}+\dfrac{7}{3}\right)+\dfrac{-5}{4}-2\\ B=2-2+\dfrac{10}{3}-\dfrac{5}{4}\\ B=\dfrac{40}{12}-\dfrac{15}{12}=\dfrac{25}{12}\)
B= \(\left(\dfrac{-4}{5}+\dfrac{14}{5}\right)+\left(\dfrac{3}{3}+\dfrac{7}{3}\right)+\dfrac{-5}{4}-2\)
B= \(\dfrac{25}{12}\)
Giải:
\(\dfrac{\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{2}{7}\right)+\left(1-\dfrac{3}{8}\right)+...+\left(1-\dfrac{88}{93}\right)}{\dfrac{-1}{12}-\dfrac{1}{14}-\dfrac{1}{16}-...-\dfrac{1}{186}}\)
Gọi dãy là A,phần tử là B. Ta có:
B=\(\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{2}{7}\right)+\left(1-\dfrac{3}{8}\right)+...+\left(1-\dfrac{88}{93}\right)\)
B=\(\dfrac{5}{6}+\dfrac{5}{7}+\dfrac{5}{8}+...+\dfrac{5}{93}\)
B=5.\(\left(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+...+\dfrac{1}{93}\right)\)
B=5.\(\left[\dfrac{2}{2}.\left(\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+...+\dfrac{1}{93}\right)\right]\)
B=5.\(\left[2.\left(\dfrac{1}{12}+\dfrac{1}{14}+\dfrac{1}{16}+...+\dfrac{1}{186}\right)\right]\)
B=10.\(\left(\dfrac{1}{12}+\dfrac{1}{14}+\dfrac{1}{16}+...+\dfrac{1}{186}\right)\)
⇒A=\(\dfrac{10.\left(\dfrac{1}{12}+\dfrac{1}{14}+\dfrac{1}{16}+...+\dfrac{1}{186}\right)}{\dfrac{-1}{12}+\dfrac{-1}{14}+\dfrac{-1}{16}+...+\dfrac{-1}{186}}\)
⇒A=-10
Chúc bạn học tốt!
\(\left\{\left[3^{14}.69+3^{14}.12\right]:3^{16}-7\right\}:2^4\\ =\left[3^{14}\left(69+12\right):3^{16}-7\right]:2^4=\left[\left(3^{14}.3^4\right):3^{16}-7\right]:2^4\\ =\left(3^2-7\right):2^4=\left(9-7\right):2^4=2:2^4=\dfrac{1}{8}\)
Bạn ơi! Bạn viết sai dấu ngoặc nhé! Mình sửa thành:
[(314. 69 + 314. 12) : 316 - 7] : 24
= {[ 314. (69 + 12)] : 316 - 7} : 24
= {[ 314. 81] : 316 - 7} : 24
= {[314. 34] : 316 - 7} : 24
= {318 : 316 - 7} : 24
= {32 - 7} : 24
= {9 - 7} : 24
= 2 : 16
= \(\dfrac{1}{8}\)
= 8.