cái này toán lớp 6 nha
A=1/17.(17/1.18+.....+1/200/2017)
A=1/17.(1-1/2017)
B=1/2000.(200/1.2001+....+2000/17.2017)
B=1/2000.(1-1/2017)
=> A/B=1/17.(1-2017)/1/2000.(1-1/2017)=1/17.2000
a, Cho a + b + c =0 chứng minh:
\(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}=|\frac{1}{a}+\frac{1}{b}+\frac{1}{c}|\)
b, Tính
\(A=\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+...+\sqrt{1+\frac{1}{399^2}+\frac{1}{400^2}}\)
bài 1 cho a+b+c=0. CMR:
\(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}=|\frac{1}{a}+\frac{1}{b}+\frac{1}{c}|\)
áp dụng tính :
M=\(\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...\sqrt{1+\frac{1}{99^2}+\frac{1}{100^2}}\)
cho a;b;c sao cho abc=1.CMR:\(a+b+c+\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\)
cho a,b,c>0
CMR:
\(\left(a+b+\frac{1}{2}\right)^2+\left(b+c+\frac{1}{2}\right)^2+\left(c+a+\frac{1}{2}\right)^2\ge4\left(\frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{b}+\frac{1}{c}}+\frac{1}{\frac{1}{c}+\frac{1}{a}}\right)\)
cho a,b,c>0 . CMR :
\(\left(a+b+\frac{1}{2}\right)^2+\left(b+c+\frac{1}{2}\right)^2+\left(c+a+\frac{1}{2}\right)^2\ge4\left(\frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{b}+\frac{1}{c}}+\frac{1}{\frac{1}{c}+\frac{1}{a}}\right)\)
1) Cho các số a,b,c thỏa mãn: a+b+c=3;\(\frac{1}{2a^2}+\frac{1}{2b^2}+\frac{1}{2c^2}+\frac{3}{2}=\frac{\sqrt{2b-1}}{a}+\frac{\sqrt{2c-1}}{b}+\frac{\sqrt{2a-1}}{c}\)
Tính M=\(\frac{\left(a+1\right)^2}{ab+1}+\frac{\left(b+1\right)^2}{bc+1}+\frac{\left(c+1\right)^2}{ca+1}\)
Cho a,b,c\(\ge\)0. CM
\(\left(a+b+\frac{1}{4}\right)^2+\left(b+c+\frac{1}{4}\right)^2+\left(c+a+\frac{1}{4}\right)^2\ge4\left(\frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{b}+\frac{1}{c}}+\frac{1}{\frac{1}{c}+\frac{1}{a}}\right).\)
Các bạn ơi giúp mk với:
Cho \(M=\frac{1}{7+\frac{1}{5+\frac{1}{3+\frac{1}{2}}}}+\frac{1}{9+\frac{1}{8+\frac{1}{7+\frac{1}{6}}}}\) và \(N=\frac{1}{3+\frac{1}{5+\frac{1}{7+\frac{1}{a+\frac{1}{b}}}}}\)
a) Tính giá trị của M viết dưới dạng phân số
b) Tìm các số tự nhiên a,b biết \(N=\frac{3655}{11676}\)
a/ Cho a+b+c=0
CMR:\(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}=\left[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right]\)
P/s: [] là giá trị tuyệt đối
Ap dụng tính:
\(S=\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}.......+\sqrt{1+\frac{1}{99^2}+\frac{1}{100^2}}\)
