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Rút gọn bt: A = \(\dfrac{\left(1^4+4\right)\left(5^4+4\right)\left(9^4+4\right)...\left(21^4+4\right)}{\left(3^4+4\right)\left(7^4+4\right)\left(11^4+4\right)...\left(23^4+4\right)}\)
B = \(\left(\dfrac{n-1}{1}+\dfrac{n-2}{2}+\dfrac{n-3}{3}+..+\dfrac{2}{n-2}+\dfrac{1}{n-1}\right):\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{n}\right)\)
Rút gọn
A=\(\dfrac{\left(1^4+\dfrac{1}{4}\right)\left(3^4+\dfrac{1}{4}\right)\left(5^4+\dfrac{1}{4}\right)...\left(11^4+\dfrac{1}{4}\right)}{\left(2^4+\dfrac{1}{4}\right)\left(4^4+\dfrac{1}{4}\right)\left(6^4+\dfrac{1}{4}\right)...\left(12^4+\dfrac{1}{4}\right)}\)
\(\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{8}\right).\left(1+\dfrac{1}{15}\right).......\left(1+\dfrac{1}{n^2+2n}\right)\)
YT
5 tháng 12 2017 lúc 11:11
Tính giá trị biểu thức :
\(A=\dfrac{\left(1+\dfrac{1}{4}\right)\left(3^4+\dfrac{1}{4}\right)\left(5^4+\dfrac{1}{4}\right).....\left(29^4+\dfrac{1}{4}\right)}{\left(2^4+\dfrac{1}{4}\right)\left(4^4+\dfrac{1}{4}\right)\left(6^4+\dfrac{1}{4}\right).....\left(30^4+\dfrac{1}{4}\right)}\)
T^T
\(\dfrac{1}{\left(a-b\right)\left(b-c\right)}+\dfrac{1}{\left(b-c\right)\left(c-a\right)}\dfrac{1}{\left(c-a\right)\left(a-b\right)}\)
Tính
a)left(dfrac{left(x-1right)^2}{left(3x+x-1right)^2}-dfrac{1-2x^2+4x}{x^3-1}+dfrac{1}{x-1}right):dfrac{x^2+x}{x^2+1}
b)left(dfrac{3left(x+2right)}{2left(x^3+x^2+x+1right)}+dfrac{2x^2-x+10}{2left(x^3+x^2+x+1right)}right):left(dfrac{5}{x^2+1}+dfrac{3}{2left(x+1right)}-dfrac{3}{2left(x-1right)}right).dfrac{2}{x-1}
c)left(dfrac{x^2}{x^2-5x+6}+dfrac{x^2}{x^2-3x+2}right):dfrac{left(x-1right)left(x-3right)}{x^4+x^2+1}
Đọc tiếp
Tính
a)\(\left(\dfrac{\left(x-1\right)^2}{\left(3x+x-1\right)^2}-\dfrac{1-2x^2+4x}{x^3-1}+\dfrac{1}{x-1}\right):\dfrac{x^2+x}{x^2+1}\)
b)\(\left(\dfrac{3\left(x+2\right)}{2\left(x^3+x^2+x+1\right)}+\dfrac{2x^2-x+10}{2\left(x^3+x^2+x+1\right)}\right):\left(\dfrac{5}{x^2+1}+\dfrac{3}{2\left(x+1\right)}-\dfrac{3}{2\left(x-1\right)}\right).\dfrac{2}{x-1}\)
c)\(\left(\dfrac{x^2}{x^2-5x+6}+\dfrac{x^2}{x^2-3x+2}\right):\dfrac{\left(x-1\right)\left(x-3\right)}{x^4+x^2+1}\)
a) dfrac{1}{left(x-yright)left(y-zright)}+dfrac{1}{left(y-zright)left(z-xright)}+dfrac{1}{left(z-xright)left(x-yright)}
b) dfrac{1}{xleft(x-yright)left(x-zright)}+dfrac{1}{yleft(y-zright)left(y-xright)}+dfrac{1}{zleft(z-xright)left(z-yright)}
c) dfrac{x^2}{left(x-yright)left(x-zright)}+dfrac{y^2}{left(y-xright)left(y-zright)}+dfrac{z^2}{left(z-xright)left(z-yright)}
Đọc tiếp
a) \(\dfrac{1}{\left(x-y\right)\left(y-z\right)}+\dfrac{1}{\left(y-z\right)\left(z-x\right)}+\dfrac{1}{\left(z-x\right)\left(x-y\right)}\)
b) \(\dfrac{1}{x\left(x-y\right)\left(x-z\right)}+\dfrac{1}{y\left(y-z\right)\left(y-x\right)}+\dfrac{1}{z\left(z-x\right)\left(z-y\right)}\)
c) \(\dfrac{x^2}{\left(x-y\right)\left(x-z\right)}+\dfrac{y^2}{\left(y-x\right)\left(y-z\right)}+\dfrac{z^2}{\left(z-x\right)\left(z-y\right)}\)
Bài 1: CMR giá trị mỗi biểu thức sau không phụ thuộc vào giá trị ẩn:
Cdfrac{x}{xy+x+1}+dfrac{y}{yz+y+1}+dfrac{z}{zx+z+1}với xyz1
Bài 2: CMR
a, dfrac{left(x-bright)left(x-cright)}{left(a-bright)left(a-cright)}+dfrac{left(x-cright)left(x-aright)}{left(b-cright)left(b-aright)}+dfrac{left(x-aright)left(x-bright)}{left(c-aright)left(c-bright)}1
b, Nếu dfrac{1}{a}+dfrac{1}{b}+dfrac{1}{c}dfrac{1}{a+b+c}thì dfrac{1}{a^{2017}}+dfrac{1}{b^{2017}}+dfrac{1}{c^{2017}}dfrac{1}{a^{2017}+b^{2017}+c^{2017}}
Đọc tiếp
Bài 1: CMR giá trị mỗi biểu thức sau không phụ thuộc vào giá trị ẩn:
C=\(\dfrac{x}{xy+x+1}+\dfrac{y}{yz+y+1}+\dfrac{z}{zx+z+1}\)với xyz=1
Bài 2: CMR
a, \(\dfrac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\dfrac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}+\dfrac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)}=1\)
b, Nếu \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{1}{a+b+c}\)thì \(\dfrac{1}{a^{2017}}+\dfrac{1}{b^{2017}}+\dfrac{1}{c^{2017}}=\dfrac{1}{a^{2017}+b^{2017}+c^{2017}}\)
Tính các tổng sau :
a, \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+......+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\)
b, \(\dfrac{1}{1.5}+\dfrac{1}{5.9}+\dfrac{1}{9.11}+........+\dfrac{1}{\left(4n-3\right)\left(4n+1\right)}\)
c,\(\dfrac{7}{1.8}+\dfrac{7}{8.15}+\dfrac{7}{15.22}+....+\dfrac{1}{\left(7n-6\right)\left(7n+1\right)}+\dfrac{1}{7n+1}\)