(\(\dfrac{1}{9}\) - 1) . (\(\dfrac{1}{16}\) - 1) . (\(\dfrac{1}{25}\) - 1) .....(\(\dfrac{1}{361}-1\)).(\(\dfrac{1}{400}-1\))
Tính nhanh:
\(A=\left(1-\dfrac{1}{9}\right)\)x \(\left(1-\dfrac{1}{16}\right)\)x \(\left(1-\dfrac{1}{25}\right)\)x.......... x \(\left(1-\dfrac{1}{361}\right)\)x \(\left(1-\dfrac{1}{400}\right)\)
Ta có :
\(A=\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)\left(1-\dfrac{1}{25}\right)...............\left(1-\dfrac{1}{361}\right)\left(1-\dfrac{1}{400}\right)\)
\(\Rightarrow A=\left(\dfrac{9}{9}-\dfrac{1}{9}\right)\left(\dfrac{16}{16}-\dfrac{1}{16}\right)\left(\dfrac{25}{25}-\dfrac{1}{25}\right).............\left(\dfrac{361}{361}-\dfrac{1}{361}\right)\left(\dfrac{400}{400}-\dfrac{1}{400}\right)\)\(\Rightarrow A=\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}................\dfrac{360}{361}.\dfrac{399}{400}\)
\(\Rightarrow A=\dfrac{2.4}{3^2}.\dfrac{3.5}{4^2}.\dfrac{4.6}{5^2}...............\dfrac{18.20}{19^2}.\dfrac{19.21}{20^2}\)
\(\Rightarrow A=\dfrac{\left(2.3.4......19\right)\left(4.5.6......21\right)}{\left(3.4.5.....20\right)\left(3.4.5...20\right)}=\dfrac{2.21}{3.20}=\dfrac{7}{10}\)
\(A=\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)\left(1-\dfrac{1}{25}\right)...\left(1-\dfrac{1}{361}\right)\left(1-\dfrac{1}{400}\right)\)
\(A=\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}...\dfrac{360}{361}.\dfrac{399}{400}\)
\(A=\dfrac{2.4}{3^2}.\dfrac{3.5}{4^4}.\dfrac{4.6}{5^2}...\dfrac{18.20}{19^2}.\dfrac{19.21}{20^2}\)
\(A=\dfrac{2.3.4...18.19}{3.4.5...20}.\dfrac{4.5.6...21}{3.4.5....20}\)
\(A=\dfrac{1}{10}.7=\dfrac{7}{10}\)
Bài 1. Thực hiện phép tính:
a) |5.0,6+\(\dfrac{2}{3}\)|- \(\dfrac{1}{3}\)
b)(0,25 - 1\(\dfrac{1}{4}\)) : 5 - \(\dfrac{1}{5}\).(-3)\(^2\)
c)\(\dfrac{14}{17}.\dfrac{7}{5}-\dfrac{-3}{17}:\dfrac{5}{7}\)
d)\(\dfrac{7}{16}+\dfrac{-9}{25}+\dfrac{9}{16}+\dfrac{-16}{25}\)
e)\(\dfrac{5}{6}+2\sqrt{\dfrac{4}{9}}\)
a) Ta có: \(\left|5\cdot0.6+\dfrac{2}{3}\right|-\dfrac{1}{3}\)
\(=\left|3+\dfrac{2}{3}\right|-\dfrac{1}{3}\)
\(=3+\dfrac{2}{3}-\dfrac{1}{3}\)
\(=3+\dfrac{1}{3}=\dfrac{10}{3}\)
b) Ta có: \(\left(0.25-1\dfrac{1}{4}\right):5-\dfrac{1}{5}\cdot\left(-3\right)^2\)
\(=\left(\dfrac{1}{4}-\dfrac{5}{4}\right)\cdot\dfrac{1}{5}-\dfrac{1}{5}\cdot9\)
\(=\dfrac{-4}{4}\cdot\dfrac{1}{5}-\dfrac{1}{5}\cdot9\)
\(=\dfrac{1}{5}\cdot\left(-1-9\right)\)
\(=-10\cdot\dfrac{1}{5}=-2\)
c) Ta có: \(\dfrac{14}{17}\cdot\dfrac{7}{5}-\dfrac{-3}{17}:\dfrac{5}{7}\)
\(=\dfrac{14}{17}\cdot\dfrac{7}{5}-\dfrac{-3}{17}\cdot\dfrac{7}{5}\)
\(=\dfrac{7}{5}\cdot\left(\dfrac{14}{17}+\dfrac{3}{17}\right)\)
\(=\dfrac{7}{5}\cdot1=\dfrac{7}{5}\)
d) Ta có: \(\dfrac{7}{16}+\dfrac{-9}{25}+\dfrac{9}{16}+\dfrac{-16}{25}\)
\(=\left(\dfrac{7}{16}+\dfrac{9}{16}\right)-\left(\dfrac{9}{25}+\dfrac{16}{25}\right)\)
\(=\dfrac{16}{16}-\dfrac{25}{25}\)
\(=1-1=0\)
e) Ta có: \(\dfrac{5}{6}+2\sqrt{\dfrac{4}{9}}\)
\(=\dfrac{5}{6}+2\cdot\dfrac{2}{3}\)
\(=\dfrac{5}{6}+\dfrac{4}{3}\)
\(=\dfrac{5}{6}+\dfrac{8}{6}=\dfrac{13}{6}\)
Tính
B = \(\left(\dfrac{1}{4}-1\right)+\left(\dfrac{1}{9}-1\right)+\left(\dfrac{1}{16}-1\right)....\left(\dfrac{1}{400}-1\right)\)
Sửa đề: \(B=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\left(\dfrac{1}{16}-1\right)\cdot...\cdot\left(\dfrac{1}{400}-1\right)\)
Ta có: \(B=\left(\dfrac{1}{4}-1\right)\left(\dfrac{1}{9}-1\right)\left(\dfrac{1}{16}-1\right)\cdot...\cdot\left(\dfrac{1}{400}-1\right)\)
\(=\dfrac{-3}{4}\cdot\dfrac{-8}{9}\cdot\dfrac{-15}{16}\cdot...\cdot\dfrac{-399}{400}\)
\(=\dfrac{-3\cdot8\cdot15\cdot...\cdot399}{4\cdot9\cdot16\cdot...\cdot400}\)
\(=\dfrac{-3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot19\cdot21}{2^2\cdot3^2\cdot4^2\cdot...\cdot20^2}\)
\(=\dfrac{-2\cdot3\cdot4\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\cdot\dfrac{3\cdot4\cdot5\cdot...\cdot21}{2\cdot3\cdot4\cdot20}\)
\(=\dfrac{-1}{20}\cdot\dfrac{21}{2}\)
\(=\dfrac{-21}{40}\)
Tìm A biết: A\(\times\)(1-\(\dfrac{1}{4}\))\(\times\)(1-\(\dfrac{1}{9}\))\(\times\)(1-\(\dfrac{1}{16}\))\(\times\)(1-\(\dfrac{1}{25}\))=1\(\dfrac{3}{5}\)
\(A\cdot\left(1-\dfrac{1}{4}\right)\cdot\left(1-\dfrac{1}{9}\right)\cdot\left(1-\dfrac{1}{16}\right)\left(1-\dfrac{1}{25}\right)=1\dfrac{3}{5}\)
=>\(A\cdot\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{5}\right)\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)\left(1+\dfrac{1}{5}\right)=\dfrac{8}{5}\)
=>\(A\cdot\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot\dfrac{6}{5}=\dfrac{8}{5}\)
=>\(A\cdot\dfrac{1}{5}\cdot\dfrac{6}{2}=\dfrac{8}{5}\)
=>\(A\cdot3=8\)
=>A=8/3
\(A=\left(2\dfrac{1}{3}+3\dfrac{1}{2}\right):\left(-4\dfrac{1}{6}+3\dfrac{1}{7}\right)+7\dfrac{1}{2}\)
\(B=4\dfrac{25}{16}+25\cdot\left(\dfrac{9}{16}:\dfrac{125}{64}\right):\left(-\dfrac{27}{8}\right)\)
giải hộ mk nhanh nhanh nhoa ☺
Tính giá trị của các biểu thức sau 1) \(A=1+2+2^2+...+2^{2015}\) 2) \(B=\left(\dfrac{1}{4}-1\right)\cdot\left(\dfrac{1}{9}-1\right)\cdot\left(\dfrac{1}{16}-1\right)\cdot\cdot\cdot\cdot\cdot\left(\dfrac{1}{400}-1\right)\) 3) \(C=\left(\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+\dfrac{1}{14\cdot19}+...+\dfrac{1}{44\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\) 4) \(D=\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\) 5) \(E=\dfrac{\dfrac{1}{2003}+\dfrac{1}{2004}-\dfrac{1}{2005}}{\dfrac{5}{2003}+\dfrac{5}{2004}-\dfrac{5}{2005}}-\dfrac{\dfrac{2}{2002}+\dfrac{2}{2003}-\dfrac{2}{2004}}{\dfrac{3}{2002}+\dfrac{3}{2003}-\dfrac{3}{2004}}\) 6) Cho 13+23+...+103=3025 Tính S= 23+43+63+...+203
a,2.(\(\dfrac{1}{4}\)+x)\(^3\)=(\(-\dfrac{27}{4}\))
b,(x+\(\dfrac{1}{2}\))\(^3\):3=\(\dfrac{-1}{81}\)
c,(\(\dfrac{2}{3}\)-x)\(^2\)=1:\(\dfrac{4}{9}\)
d,(2x-\(\dfrac{1}{5}\))\(^2\)+\(\dfrac{16}{25}\)=1
e,(\(\dfrac{2}{5}\)-3x)\(^2\)-\(\dfrac{1}{5}\)=\(\dfrac{4}{25}\)
Tính giá trị biểu thức sau bằng cách thuận tiện nhất và kết quả dưới dạng số thập phân
\(1\dfrac{1}{10}\)+\(1\dfrac{4}{20}\)+\(1\dfrac{9}{30}\)+\(1\dfrac{16}{40}\)+\(1\dfrac{25}{50}\)+\(1\dfrac{36}{60}\)+\(1\dfrac{49}{70}\)+\(1\dfrac{64}{80}\)+\(1\dfrac{81}{90}\)
giúp mik với mik cần gấp
= 1,1 + 1,2 + 1,3 + 1,4 + 1,5 + 1,6 + 1,7 + 1,8 + 1,9
= 2,3 + 1,3 + 1,4 + 1,5 + 1,6 + 1,7 + 1,8 + 1,9
= 3,6 + 1,4 + 1,5 + 1,6 + 1,7 + 1,8 + 1,9
= 5 + 1,5 + 1,6 + 1,7 + 1,8 + 1,9
= 6,5 + 1,6 + 1,7 + 1,8 + 1,9
= 8,1 + 1,7 + 1,8 + 1,9
= 9,8 + 1,8 + 1,9
= 11,6 + 1,9
= 13,5
Tính giá trị biểu thức sau bằng cách thuận tiện nhất và kết quả dưới dạng số thập phân
\(1\dfrac{1}{10}\)+\(1\dfrac{4}{20}\)+\(1\dfrac{9}{30}\)+\(1\dfrac{16}{40}\)+\(1\dfrac{25}{50}\)+\(1\dfrac{36}{60}\)+\(1\dfrac{49}{70}\)+\(1\dfrac{64}{80}\)+\(1\dfrac{81}{90}\)