ta có 1/2^2<1/2
1/2^3<1/2
.............
1/2^50<1/2
\(\Rightarrow\)1/2*50>1/2^1+1/2^2+1/2^3+...........+1/2^50
\(\Rightarrow\)
ta có 1/2^2<1/2
1/2^3<1/2
.............
1/2^50<1/2
\(\Rightarrow\)1/2*50>1/2^1+1/2^2+1/2^3+...........+1/2^50
\(\Rightarrow\)
1.So sánh: A=\(\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\) và 1:
So sánh :
\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\)và 1
Tính và so sánh: \(S=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}...+\frac{99}{49^2.50^2}\)\(T=\frac{1}{2^2-1^2}+\frac{1}{3^2-1^2}+\frac{1}{4^2-1^2}+...+\frac{1}{50^2-1^2}\)
\(A=\frac{\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{49}+\frac{1}{50}}{\frac{100}{1}+\frac{49}{2}+...+\frac{2}{49}+\frac{1}{50}}\)= ?
So sánh :
\(1\) và \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{50}}\)
e, \(\frac{49}{1}+\frac{48}{2}+\frac{47}{3}+.......+\frac{2}{48}+\frac{1}{49}=50.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.......+\frac{1}{50}\right)\)
Cho A =\(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{49.50}\)
B=\(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}\)
C=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{49}+\frac{1}{50}\)
Chứng minh A = B - 2C
So sánh :
a) 3-50 và 5-30
b)\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\) và \(B=\frac{1}{2}\)
so sánh \(\frac{2^{47}+1}{2^{49}+1}và\frac{2^{42}+1}{2^{44}+1}\)
so sánh : \(2^{69}và5^{31}\)