;-;

\(S=\dfrac{1}{50}+\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{98}+\dfrac{1}{99}\)

\(S=\dfrac{1}{50}>100\)    \(\dfrac{1}{51}>100\)   \(\dfrac{1}{52}>100\)   \(....\)   \(\dfrac{1}{98}>100\)    \(\dfrac{1}{99}>100\)

\(\Rightarrow S>\dfrac{1}{100}+\dfrac{1}{100}+\dfrac{1}{100}+...+\dfrac{1}{100}+\dfrac{1}{100}\\ \) {50 số 100}

\(S>50\cdot\dfrac{1}{100}=\dfrac{1}{2}\)

\(S>\dfrac{1}{2}\)

a: \(A=\left(\dfrac{1}{99}+1\right)+\left(\dfrac{2}{98}+1\right)+...+\left(\dfrac{98}{2}+1\right)+1\)

\(=\dfrac{100}{99}+\dfrac{100}{98}+...+\dfrac{100}{2}+\dfrac{100}{100}\)

\(=100\cdot\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{100}\right)\)=100B

=>B/A=1/100

b: \(A=\left(\dfrac{1}{49}+1\right)+\left(\dfrac{2}{48}+1\right)+\left(\dfrac{3}{47}+1\right)+...+\left(\dfrac{48}{2}+1\right)+\left(1\right)\)

\(=\dfrac{50}{49}+\dfrac{50}{48}+....+\dfrac{50}{2}+\dfrac{50}{50}\)

\(=50\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{50}\right)\)

\(B=\dfrac{2}{2}+\dfrac{2}{3}+\dfrac{2}{4}+...+\dfrac{2}{49}+\dfrac{2}{50}\)

\(=2\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{49}+\dfrac{1}{50}\right)\)

=>A/B=25

Bài 3: a) Xét A=(1+1/2+1/3+....+1/98).2.3.4.5.....98

=(1+1/2+1/3+....+1/98).(9.11).2.3.4.....98

=(1+1/2+1/3+....+1/98).99.2.3.4....98⋮99
(đpcm)

\(\frac{N}{2}=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}\)

\(\frac{N}{2}=N-\frac{N}{2}=\frac{1}{2}-\frac{1}{2^{100}}\Rightarrow N=1-\frac{1}{2^{99}}

tính B

a) Đặt M=1/2+1/2²+1/2³+...+1/2¹⁹⁹⁸

=>2M=1+1/2+1/2²+1/2³+...+1/2¹⁹⁹⁷

2M-M=(1+1/2+1/2²+1/2³+...+1/2¹⁹⁹⁷)-(1/2+1/2²+1/2³+...+1/2¹⁹⁹⁸)

M=1-1/2¹⁹⁹⁸