\(Cho\) \(\frac{a}{5}\)=\(\frac{b}{4}=\frac{c}{3}\) va abc= -480.tim a,b,c
(cac ban giai chi tiet giup minh nhe)
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So sanh
\(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{90}+\frac{1}{100}.\)va 100
cac ban giai chi tiet giup mk voi
Bạn sai đè thì phải,đúng phải là 1/99
Ta thấy:Từ 1->1/100 có 100 số.
Ta có:100=1.100
Vì 1=1 ;1/2<1 ;1/3<1 ;1/4<1 ;... ;1/90<1 ;1/100<1.
\(\Rightarrow1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{99}+\frac{1}{100}< 1.100=100\)
\(\Rightarrow1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{99}+\frac{1}{100}< 100\)
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Tim gia tri lon nhat cua
\(B=\frac{4}{4x^2+12x+14}\)
xin loi de bai lan truoc minh danh sai nhe cac ban.Mau giai chi tiet giup minh voi minh dang can gap lam
\(4x^2+12x+14=\left(2x\right)^2+2.2x.3+3^2+5=\left(2x+3\right)^2+5\ge5>0\)
\(\Rightarrow B\le\frac{4}{5}\)
Dấu "=" xảy ra khi \(2x+3=0\Leftrightarrow x=-\frac{3}{2}\)
Vậy GTLN của B là \(\frac{4}{5}\)
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Tim GTNN cua bt sau
a, lx-2l + l x+28l + lx-60l
b, lxl + lx-1l + lx-2l+...+lx-2004l
Cac ban giai chi tiet giup minh nhe, minh dang can gap.
\(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+....+\frac{1}{\sqrt{99}+\sqrt{100}}\)
giup minh voi
cam on nhieu
cac ban giai chi tiet giup minh nha
\(\frac{1}{\sqrt{a}+\sqrt{a+1}}=\frac{\sqrt{a+1}-\sqrt{a}}{\left(\sqrt{a}+\sqrt{a+1}\right)\left(\sqrt{a+1}-\sqrt{a}\right)}=\frac{\sqrt{a+1}-\sqrt{a}}{a+1-a}=\sqrt{a+1}-\sqrt{a}\Rightarrow\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+.......+\frac{1}{\sqrt{99}+\sqrt{100}}=-1+\sqrt{2}-\sqrt{2}+\sqrt{3}-......-\sqrt{99}+\sqrt{100}=10-1=9\)
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Tinh:
\(A=1+\frac{3}{2^3}+\frac{4}{2^4}+\frac{5}{2^5}+...+\frac{100}{2^{100}}\)
cac ban giai chi tiet ra nha
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) \(-\frac{5}{11}+2x=\frac{7}{22}\)
\(2x=\frac{7}{22}+\frac{5}{11}\)
\(2x=\frac{17}{22}\)
\(x=\frac{17}{22}:2\)
\(x=\frac{17}{44}\)
\(x=-\frac{1}{5}:5\)
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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!!!
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bài 1: cho a,b,c>0 và a+b+c=1
CMR: \(\frac{a}{1+b-a}+\frac{b}{1+c-b}+\frac{c}{1+a-c}>=1\)
bai2 cho a,b,c>0
CMR \(\frac{bc}{a}+\frac{ac}{a}+\frac{ab}{c}>=a+b+c\)
cac ban oi giup minhdi. minh lam chuyen con 2 bai nay minh chua mlam dc. cac ban giup minh nhe. minh dang can lam
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)
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Cho a,b,c là các số nguyên dương đôi một khác nhau. Cmr: (a-b)5+(b-c)5+(c-a)5 chia hết cho 5(a-b)(b-c)(c-a)
cac ban giup minh giai chi tiet voi minh like cho
Đặt \(x=a-b,y=b-c,z=c-a\to x+y+z=0.\) Ta có
\(\left(a-b\right)^5+\left(b-c\right)^5+\left(c-a\right)^5=x^5+y^5+z^5=x^5+y^5+\left(-x-y\right)^5=x^5+y^5-\left(x+y\right)^5.\)
Mà \(\left(x+y\right)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5,\) suy ra
\(\left(a-b\right)^5+\left(b-c\right)^5+\left(c-a\right)^5=x^5+y^5-\left(x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5\right)\)
\(=-\left(5x^4y+10x^3y^2+10x^2y^3+5xy^4\right)=-5xy\left(x^3+2x^2y+2xy^2+y^3\right)\)
\(=-5xy\left(x+y\right)\left(x^2+xy+y^2\right)=5xyz\left(x^2+xy+y^2\right)\vdots5xyz=5\left(a-b\right)\left(b-c\right)\left(c-a\right).\)
Suy ra điều phải chứng minh.
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