Đặt \(A=\frac{1}{2}+\frac{1}{2^2}+......+\frac{1}{2^{50}}\)
\(2A=1+\frac{1}{2}+...+\frac{1}{2^{49}}\)
\(2A-A=1-\frac{1}{2^{50}}\)
\(A=1-\frac{1}{2^{50}}< 1\)
\(\Rightarrow A< 1\)
1.So sánh: A=\(\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\) và 1:
1.So sánh: A=\(\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\) và 1:
Tính và so sánh: \(S=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}...+\frac{99}{49^2.50^2}\)\(T=\frac{1}{2^2-1^2}+\frac{1}{3^2-1^2}+\frac{1}{4^2-1^2}+...+\frac{1}{50^2-1^2}\)
\(A=\frac{\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{49}+\frac{1}{50}}{\frac{100}{1}+\frac{49}{2}+...+\frac{2}{49}+\frac{1}{50}}\)= ?
e, \(\frac{49}{1}+\frac{48}{2}+\frac{47}{3}+.......+\frac{2}{48}+\frac{1}{49}=50.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.......+\frac{1}{50}\right)\)
So sánh :
\(1\) và \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{50}}\)
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 \(B=\frac{1}{2}\)
Cho B=\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2^{99}}\) ,So sánh B với 50
So sánh:
1)A= \(\frac{1}{2}\)+\(\frac{1}{2^2}\) + \(\frac{1}{2^3}\)+....+\(\frac{1}{2^{49}}\)+ \(\frac{1}{2^{50}}\)với 1
2) B=\(\frac{1}{3}\)+\(\frac{1}{3^2}\)+\(\frac{1}{3^3}\)+....+\(\frac{1}{3^{99}}\)+\(\frac{1}{2^{100}}\)với \(\frac{1}{2}\)
3)C= \(\frac{1}{4}\)+\(\frac{1}{4^2}\)+\(\frac{1}{4^3}\)+.....+\(\frac{1}{4^{999}}\)+ \(\frac{1}{4^{1000}}\)với \(\frac{1}{3}\)
