(a-4)(a+1)>0
ai làm đúng mình sẽ tich cho!^_^
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Ta co :\(M-N=\left(a+b-1\right)-\left(b+c-1\right)\)
\(M-N=a+b-1-b-c+1\)
\(M-N=\left(a-c\right)+\left(b-b\right)+\left(1-1\right)\)
\(M-N=a-c+0+0\)
\(M-N=a-c\)
Vi M>N \(\Rightarrow\) M-N la so nguyen duong \(\Rightarrow\) hieu a-c la so nguyen duong
TICK CHO MINH NHA .MINH LA NGUOI GIAI NHANH NHAT DO VA RAT CHI TIET TICK NHA BAN!!!!!!
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}\)
\(=\frac{2}{2\text{x}3}+\frac{2}{3\text{x}4}+\frac{2}{4\text{x}5}+\frac{2}{5\text{x}6}+\frac{2}{6\text{x}7}+\frac{2}{7\text{x}8}\)
\(=2\text{x}\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\right)\)
\(=2\text{x}\left(\frac{1}{2}-\frac{1}{8}\right)\)
\(=2\text{x}\frac{3}{8}=\frac{3}{4}\)
\(A=\frac{1}{\frac{3.4}{2}}+\frac{1}{\frac{4.5}{2}}+...+\frac{1}{\frac{19.20}{2}}\)
=> \(A=\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{19.20}\)
=> \(\frac{A}{2}=\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)
=> \(\frac{A}{2}=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)
=> \(\frac{A}{2}=\frac{1}{3}-\frac{1}{20}\)
=> \(\frac{A}{2}=\frac{20-3}{20.3}\)
=> \(\frac{A}{2}=\frac{17}{60}\)
=> \(A=\frac{17}{30}\)
VẬY \(A=\frac{17}{30}\)
Ta có :\(\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+19}\)
\(=\frac{1}{3\times4}\times2+\frac{1}{4\times5}\times2+...+\frac{1}{19\times20}\times2\)
\(=2\times\left(\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{19\times20}\right)=2\times\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2\times\left(\frac{1}{3}-\frac{1}{20}\right)=2\times\frac{17}{60}=\frac{17}{30}\)
Ta có : \(\frac{1}{2}< \frac{2}{3};\frac{3}{4}< \frac{4}{5};\frac{5}{6}< \frac{6}{7};...;\frac{199}{200}< \frac{200}{201}\)
Đặt \(B=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{200}{201}\)
Nên \(A< B\)
\(\Rightarrow A.B=\left(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{199}{200}\right)\left(\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{200}{201}\right)\)
\(\Rightarrow A.B=\frac{1}{201}\)
Vì \(A< B\)
\(\Rightarrow A^2< A.B=\frac{1}{201}\)
\(\Rightarrow A^2< \frac{1}{201}\)
\(\RightarrowĐPCM\)
Trả lời : Một phút suy tư bằng mội năm không phai(số 5 dịch sang Tiếng Anh là five)
Hok_Tốt
#Thiên_Hy
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{100}-\frac{1}{200}+\frac{1}{200}-\frac{1}{400}\)
\(A=1-\frac{1}{400}\)
\(A=\frac{399}{400}\)
(a-4)(a+1)>0 \(\Leftrightarrow\hept{\begin{cases}a-4>0\\a+1>0\end{cases}}\Rightarrow a=5\)
nhầm nha bn \(a\ge5\)