3 tháng 1 2019 lúc 17:21
Violympic toán 9
Các câu hỏi tương tự
Tính các tổng sau:
Adfrac{1}{2.5}+dfrac{1}{5.8}+dfrac{1}{8.11}+.....+dfrac{1}{left(3n-1right)left(3n+2right)}
Bdfrac{1}{1.3.5}+dfrac{1}{3.5.7}+dfrac{1}{5.7.9}+....+dfrac{1}{left(2n-1right)left(2n+1right)left(2n+3right)}
Csqrt{1+dfrac{1}{1^2}+dfrac{1}{2^2}}+sqrt{1+dfrac{1}{2^2}+dfrac{1}{3^2}}+sqrt{1+dfrac{1}{3^2}+dfrac{1}{4^2}}+....+sqrt{1+dfrac{1}{2018^2}+dfrac{1}{2019^2}}
Đọc tiếp
Tính các tổng sau:
A=\(\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+.....+\dfrac{1}{\left(3n-1\right)\left(3n+2\right)}\)
B=\(\dfrac{1}{1.3.5}+\dfrac{1}{3.5.7}+\dfrac{1}{5.7.9}+....+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)\left(2n+3\right)}\)
C=\(\sqrt{1+\dfrac{1}{1^2}+\dfrac{1}{2^2}}+\sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{1+\dfrac{1}{3^2}+\dfrac{1}{4^2}}+....+\sqrt{1+\dfrac{1}{2018^2}+\dfrac{1}{2019^2}}\)
cmr:
\(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}....\dfrac{2n-1}{2n}\le\dfrac{1}{\sqrt{3n+1}}\left(\forall n\ge1\right)\)
Tinh tong S(n)=\(\dfrac{1}{2,5}+\dfrac{1}{5,8}+...+\dfrac{1}{\left(3n-1\right)\left(3n+2\right)}\)
Tính các tích sau:
P_1 left(1+dfrac{2}{4}right)left(1+dfrac{2}{10}right)left(1+dfrac{2}{18}right)....left(1+dfrac{2}{n^2+3n}right)
P_2 left(1+dfrac{1}{3}right)left(1+dfrac{1}{8}right)left(1+dfrac{1}{15}right)....left(1+dfrac{2}{n^2+2n}right)
P_3 left(1-dfrac{1}{1+2}right)left(1-dfrac{1}{1+2+3}right)left(1-dfrac{1}{1+2+3+4}right).....left(1-dfrac{1}{1+2+3+4+...+n}right)
P_4 dfrac{2^4+4}{4^4+4}.dfrac{6^4+4}{8^4+4}.dfrac{8^4+4}{10^4+4}....dfrac{18^4+4}{20^4+4}
Đọc tiếp
Tính các tích sau:
P\(_1\) =\(\left(1+\dfrac{2}{4}\right)\left(1+\dfrac{2}{10}\right)\left(1+\dfrac{2}{18}\right)....\left(1+\dfrac{2}{n^2+3n}\right)\)
P\(_2\) =\(\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{8}\right)\left(1+\dfrac{1}{15}\right)....\left(1+\dfrac{2}{n^2+2n}\right)\)
P\(_3\) = \(\left(1-\dfrac{1}{1+2}\right)\left(1-\dfrac{1}{1+2+3}\right)\left(1-\dfrac{1}{1+2+3+4}\right).....\left(1-\dfrac{1}{1+2+3+4+...+n}\right)\)
P\(_4\) = \(\dfrac{2^4+4}{4^4+4}.\dfrac{6^4+4}{8^4+4}.\dfrac{8^4+4}{10^4+4}....\dfrac{18^4+4}{20^4+4}\)
Chứng minh:
\(\dfrac{1}{\sqrt{1}+\sqrt{3}}+\dfrac{1}{\sqrt{5}+\sqrt{7}}+.....+\dfrac{1}{\sqrt{97}+\sqrt{99}}>\dfrac{9}{4}\)
Rút gọn các biểu thức :
A=\(\dfrac{1}{\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}}\)
B= \(\dfrac{1}{1+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{7}}+...+\dfrac{1}{\sqrt{2015}+\sqrt{2017}}\)
Bài 2: ( chỉ ghi kết quả )
a) Tìm x biết : \(\dfrac{1}{2-\dfrac{3}{4+\dfrac{5}{6-\dfrac{7}{8+\dfrac{9}{10}}}}}=\dfrac{1}{x+\dfrac{1}{3+\dfrac{1}{5}}}+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{2}}}\)
b) Tính: ( kết quả lấy 4 chữ số thập phân)
\(P=\dfrac{\sin^390^0-\cot^330^0-\cos^245^0+\tan20^0}{2\sqrt{7}+\sin108^0\cos32^0\tan64^0}\)
Rút gọn các biểu thức sau:
a) R left(dfrac{sqrt{x}+1}{sqrt{xy}+1}+dfrac{sqrt{x}left(sqrt{y}+1right)}{1-sqrt{xy}}+1right):left(1-dfrac{sqrt{x}+1}{sqrt{xy}+1}-dfrac{sqrt{x}left(sqrt{y}+1right)}{sqrt{xy}-1}right)
b) C dfrac{2sqrt{x}}{sqrt{x}+2}+dfrac{7sqrt{x}+4}{x-sqrt{x}-6}-dfrac{sqrt{x}+2}{sqrt{x}-3}
c) M left(dfrac{1}{sqrt{x}}+dfrac{sqrt{x}}{sqrt{x}+1}right):dfrac{sqrt{x}}{sqrt{x}+x}
Đọc tiếp
Rút gọn các biểu thức sau:
a) R = \(\left(\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}+\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{1-\sqrt{xy}}+1\right):\left(1-\dfrac{\sqrt{x}+1}{\sqrt{xy}+1}-\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{\sqrt{xy}-1}\right)\)
b) C = \(\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{7\sqrt{x}+4}{x-\sqrt{x}-6}-\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\)
c) M = \(\left(\dfrac{1}{\sqrt{x}}+\dfrac{\sqrt{x}}{\sqrt{x}+1}\right):\dfrac{\sqrt{x}}{\sqrt{x}+x}\)
Cho x, y, z 0 thoả mãn x+y+z2. Tìm GTNN của các biểu thức:
a) Asqrt{x^2+dfrac{1}{x^2}}+sqrt{y^2+dfrac{1}{y^2}}+sqrt{z^2+dfrac{1}{z^2}}
b) Bsqrt{x^2+dfrac{1}{y^2}+dfrac{1}{z^2}}+sqrt{y^2+dfrac{1}{z^2}+dfrac{1}{x^2}}+sqrt{z^2+dfrac{1}{x^2}+dfrac{1}{y^2}}
c) Csqrt{2x^2+dfrac{3}{y^2}+dfrac{4}{z}}+sqrt{2y^2+dfrac{3}{z^2}+dfrac{4}{x^2}}+sqrt{2z^2+dfrac{3}{x^2}+dfrac{4}{y^2}}
Đọc tiếp
Cho x, y, z > 0 thoả mãn x+y+z=2. Tìm GTNN của các biểu thức:
a) \(A=\sqrt{x^2+\dfrac{1}{x^2}}+\sqrt{y^2+\dfrac{1}{y^2}}+\sqrt{z^2+\dfrac{1}{z^2}}\)
b) \(B=\sqrt{x^2+\dfrac{1}{y^2}+\dfrac{1}{z^2}}+\sqrt{y^2+\dfrac{1}{z^2}+\dfrac{1}{x^2}}+\sqrt{z^2+\dfrac{1}{x^2}+\dfrac{1}{y^2}}\)
c) \(C=\sqrt{2x^2+\dfrac{3}{y^2}+\dfrac{4}{z}}+\sqrt{2y^2+\dfrac{3}{z^2}+\dfrac{4}{x^2}}+\sqrt{2z^2+\dfrac{3}{x^2}+\dfrac{4}{y^2}}\)