\(A>\left(\frac{1}{150}+\frac{1}{150}+...+\frac{1}{150}\right)+\left(\frac{1}{200}+\frac{1}{200}+...+\frac{1}{200}\right)\) (mỗi ngoặc có 50 số hạng)
\(;A>\left(\frac{1}{150}.50\right)+\left(\frac{1}{200}.50\right)=50.\left(\frac{1}{150}+\frac{1}{200}\right)=50.\frac{7}{600}=\frac{7}{12}\)
Chứng minh rằng:
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}=\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{200}\)
Help me!!!!!!!
Chứng minh:
A=\(\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+......+\frac{1}{109}+\frac{1}{200}>\frac{7}{12}\)
CÁC BẠN ƠI GIÚP MIK VỚI MAI MIK PHẢI NỘP RỒI
$\frac{1}{101}$$+$$\frac{1}{102}$$+$$\frac{1}{103}$$+$ $.............$ $+$$\frac{1}{200}$
So sanh
\(\frac{1}{101}\)\(+\frac{1}{102}\)\(+...+\frac{1}{199}\)\(+\frac{1}{200}\) voi \(\frac{7}{12}\)
$A$$=$$\frac{1}{101}$$+$$\frac{1}{102}$$+$$\frac{1}{103}$$+$ $.............$ $+$$\frac{1}{200}$
$CMR$: $a$, $A$$>$$\frac{7}{12}$
$b$, $A$$>$$\frac{5}{8}$
Cho A = \(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}\)
\(a,\) Chứng minh rằng \(A>\frac{7}{12}\)
b) Chứng minh : \(A>\frac{5}{8}\)
CMR: \(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}>\frac{5}{8}\)
So sánh M va N
M=\(\frac{101^{102}+1}{101^{103}+1}\)
N=\(\frac{101^{103}+1}{101^{104}+1}\)
Chứng minh :
a) \(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\) \(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{4^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\)
b)\(\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+...+\frac{1}{79}+\frac{1}{80}< \frac{7}{12}\)
c) Cho \(S=\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\)
Chứng minh \(1< S< 2\)
