tim phan nguyen cua bieu thuc sau
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{^{5^2}}+.....+\frac{1}{2014^2}\)
Những câu hỏi liên quan
1) Cho bieu thuc A=\(3+\frac{2}{x-1}\). Tinh gia tri cua bieu thuc A khi |2x-3|=1
2) Rut gon bieu thuc B=\(\frac{x}{x-1}\)-\(\frac{x-5}{x+1}\)-\(\frac{3-x}{1-x^2}\)
3) Tim cac gia tri nguyen cua x de bieu thuc \(\frac{B}{A}\)co gia tri nguyen duong
cho phan thuc A = \(\frac{2014+\frac{2013}{2}+\frac{2012}{3}+....+\frac{2}{2013}+\frac{1}{2014}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2014}+\frac{1}{2015}}\)
Tinh gia tri cua phan thuc
1.cho bieu thuc A=\(\left(\frac{2}{x-2}+\frac{1}{x+2}\right):\frac{1}{x+2}\)
a.rút gọn bieu thuc A
b.tinh gia tri cua A tại x,biet x=1
2.tim x nguyen de gia tri cua bieu thuc A nguyen
a.\(A=\frac{3}{x+2}\)
b.\(A=\frac{x+3}{x-2}\)
1) Cho bieu thuc: \(B=\left(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}\right):\frac{x+16}{\sqrt{x}+2}\left(x\ge0,x\ne16\right)\)
a) Cho bieu thuc A= \(\frac{\sqrt{x}+4}{\sqrt{x}+2}\) ; voi cac cua bieu thuc A va B da cho, hay tim cac gia tri cua x nguyen de gia tri cua bieu thuc B(A;-1) la so nguyen
Rut gon bieu thuc
\(\frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+1}+\frac{3}{3^4+3^2+1}+...+\frac{2014}{2014^4+2014^2+1}\)
Áp dụng a/(a^4+a^2+1)=1/2.(1/(a^2-a+1)-1/(a^2+a+1)) ta được
A=1/2.(1/(1^2-1+1)-1/(1^2+1+1)+1/(2^2-2+1)-1/(2^2+2+10)+...+1/(2014^2-2014+1)-1/(2014^2+2014+1))
A=1/2.(1-1/(2014^2+2014+1))
A=-2029105/4058211
(CHẮC CHẮN ĐÚNG)
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cho bieu thuc A =\(\frac{a^3+2a^2-1}{a^3+2a^2+2a+1}\)
a)rut gon bieu thuc
b)chung minh rang neu a la so nguyen thi gia tri cua bieu thuc tim duoc o cau a la mot phan so toi gian
\(A=\frac{a^3+2a^2-1}{a^3+2a^2+2a+1}\)
a)rut gon bieu thuc
b)chung minh rang neu a la so nguyen thi gia tri cua bieu thuc tim duoc cua cau a la mot phan so toi gian
\(a,A=\frac{a^3+2a^2-1}{a^3+2a^2+2a+1}\)
\(=\frac{a^2\left(a+1\right)+\left(a-1\right)\left(a+1\right)}{a^2\left(a+1\right)+a\left(a+1\right)+\left(a+1\right)}\)
\(=\frac{\left(a+1\right)\left(a^2+a-1\right)}{\left(a+1\right)\left(a^2+a+1\right)}\)
\(=\frac{a^2+a-1}{a^2+a+1}\)
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\(A=\frac{a^3+2a^2-1}{a^3+2a^2+2a+1}\)
a/ Rut gon bieu thuc
b/ Chung minh rang neu a la so nguyen thi gia tri cua bieu thuc tim duoc o cau a, la mot phan so toi gian
a,Tim GTNN cua bieu thuc \(C=\left(x+2\right)^2+\left(y-\frac{1}{5}\right)^2-10\)
b,Tim GTLN cua bieu thuc \(D=\frac{4}{\left(2x-3\right)^2+5}\)
\(\text{a)Để C đạt GTNN}\)
\(\Rightarrow\hept{\begin{cases}\left(x+2\right)^2\\\left(y-\frac{1}{5}\right)^2\end{cases}\ge0}\)
\(\Rightarrow\left(x+2\right)^2+\left(y-\frac{1}{5}\right)^2\ge0\)
\(\Rightarrow\left(x+2\right)^2+\left(y-\frac{1}{5}\right)^2-10\ge0-10\)
\(\Rightarrow C\ge-10\)
\(\text{Vậy minC=-10 khi x=-2;y= }\frac{1}{5}\)
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b)\(\text{Để D đạt GTLN}\)
=>(2x-3)2+5 đạt GTNN
Mà (2x-3)2\(\ge\)5
\(\Rightarrow GTLN\)của \(A=\frac{4}{5}\)khi \(x=\frac{3}{2}\)
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