\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\)
Giup minh nhe
chung minh rang
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}=\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{200}\)
giup minh minh like cho nho giai chi tiet mot chut nhe
1-1/2+1/3-1/4+...+1/199-1/200=(1+1/2+1/3+1/4+...+199+1/200)-(1+1/2+1/3+...+1/100)=1+1/2+1/3+1/4+...+1/199+1/200-1-1/2-1/3-1/4-...-1/99-1/100=(1+1/2+1/3+...+1/100)-(1+1/2+1/3+...+1/100)+(1/101+1/102+...+1/200)=0+(1/101+1/102+...+1/200)=(1/101+1/102+...+1/200)(đpcm)
tìm x biết
a,\(|5x+\frac{3}{4}|-\frac{5}{4}=2\)
b,\(\frac{3}{2}-|\frac{1}{2}x+1|=\frac{1}{4}\)
cac ban lam on giup minh lam nhanh nhe
a/ \(\left|5x+\frac{3}{4}\right|-\frac{5}{4}=2\)
\(\left|5x+\frac{3}{4}\right|=\frac{13}{4}\)
/ \(5x+\frac{3}{4}=\frac{13}{4}\)\(\Rightarrow x=\left\{\frac{1}{2};-\frac{4}{5}\right\}\)
b/\(\frac{3}{2}-\left|\frac{1}{2}x+1\right|=\frac{1}{4}\)
\(\left|\frac{1}{2}x+1\right|=\frac{5}{4}\)
1/\(\frac{1}{2}x+1=\frac{5}{4}\)
\(\frac{1}{2}x=\frac{1}{4}\)
\(x=\frac{1}{2}\)
2/\(\frac{1}{2}x+1=-\frac{5}{4}\)
\(\frac{1}{2}x=-\frac{9}{4}\)
\(x=-\frac{9}{2}\)
\(\Rightarrow x=\left\{\frac{1}{2};-\frac{9}{2}\right\}\)
\(y=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2013^2}\)
giup minh nhe may ban
tính Y ak e,nếu tính Y thì a giúp dc
Y=1
\(\frac{12}{13^2}+12:13:14:...:120\)
cuu voi
Tinh:
\(\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{5}}{\frac{7}{6}-\frac{7}{8}+\frac{7}{10}}\)
Giup minh trinh bay cach cach giai voi nhe
Ko hieu vao phan"Doc them"
\(\frac{\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{5}\right)}{\frac{7}{2}\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{5}\right)}\)=\(\frac{1}{\frac{7}{2}}\)=\(\frac{2}{7}\)
cho 3 số a, b, c>0, và a+b+c=3. chứng minh rằng:
\(\frac{a^4}{\left(a+2\right)\left(b+2\right)}+\frac{b^4}{\left(b+2\right)\left(c+2\right)}+\frac{c^4}{\left(c+2\right)\left(a+2\right)}\ge\frac{1}{3}\)
giải giup minh nhe
Áp dụng BĐT Cosi:
\(\frac{a^4}{\left(a+2\right)\left(b+2\right)}+\frac{a+2}{27}+\frac{b+2}{27}+\frac{1}{9}>=4\sqrt[4]{\frac{\left(a+2\right)\left(b+2\right)}{27.27.9}.\frac{a^4}{\left(a+2\right)\left(b+2\right)}}...\)
\(>=\frac{4}{9}a\)
Tương tự
\(=>VT>=\frac{4}{9}\left(a+b+c\right)-\frac{3}{9}-2\left(\frac{a+2}{9}+\frac{b+2}{9}+\frac{c+2}{9}\right)=\frac{1}{3}.\)
Dấu "="xảy ra khi a=b=c=1
a)\(x-\frac{4}{5}=\frac{5}{7}\);b)\(5x=\frac{-1}{5}+\frac{11}{5}\); c)\(\frac{5}{3}-x=7+\frac{4}{5}\);d)\(\frac{-5}{11}+2x=\frac{7}{22}\)
CAC BAN GIUP MINH NHE MINH DANG CAN GAP
a) \(x-\frac{4}{5}=\frac{5}{7}\)
\(x=\frac{5}{7}+\frac{4}{5}=\frac{53}{35}\)
b) \(5x=-\frac{1}{5}\)
\(x=-\frac{1}{5}:5=-\frac{1}{25}\)
c) \(\frac{5}{3}-x=7+\frac{4}{5}\)
\(\frac{5}{3}-x=\frac{39}{5}\)
\(x=\frac{5}{3}-\frac{39}{5}=-\frac{92}{15}\)
d) \(-\frac{5}{11}+2x=\frac{7}{22}\)
\(2x=\frac{7}{22}+\frac{5}{11}\)
\(2x=\frac{17}{22}\)
\(x=\frac{17}{22}:2\)
\(x=\frac{17}{44}\)
\(x=-\frac{1}{5}:5\)
NÈ BẠN!!!
a) \(x-\frac{4}{5}=\frac{5}{7}\)
\(x=\frac{5}{7}+\frac{4}{5}=\frac{25}{35}+\frac{28}{35}=\frac{53}{35}\)
b) \(5x=-\frac{1}{5}+\frac{11}{5}\)
\(5x=2\)
\(x=\frac{2}{5}\)
c)\(\frac{5}{3}-x=7\)
\(x=\frac{5}{3}-7=\frac{5}{3}-\frac{21}{3}=-\frac{16}{3}\)
d) \(-\frac{5}{11}+2x=\frac{7}{22}\)
\(2x=\frac{7}{22}-\frac{-5}{11}=\frac{7}{22}-\frac{-10}{22}=\frac{17}{22}\)
\(x=\frac{17}{22}:2=\frac{17}{22}\cdot\frac{1}{2}=\frac{17}{44}\)
K CHO MÌNH NHA!!!
tinh \(\frac{1}{2-\sqrt{3}}-3\)
giup minh nhe mn
\(\frac{1}{2-\sqrt{3}}-3=\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}-3=\frac{2+\sqrt{3}}{4-3}-3\)\(=2+\sqrt{3}-3=\sqrt{3}-1\)
Bài 1: cho x,y thoả mãn 0<x<2 và 4<y<5 và x+y=6
Tìm Min của P= \(\frac{1}{x}+\frac{1}{y}\)
cac ban oi giup minh di minh chuan bi di hoc roi. giup minh nhe.
Cho 7 phân số
\(\frac{7}{5};\frac{4}{13};\frac{2}{13};\frac{1}{18};\frac{7}{3};\frac{4}{5};\frac{7}{4}\)
Thắn chọn được hai phân số có tổng lớn nhất. Long chọn được hai phân số có tổng bé nhất. Tính tổng 4 phân số mà Thắng và Long đã chọn ?
(giup minh nhe cac ban) (minh dang can gap)