Question

Cho

S=1/50 + 1/51 + 1/52 +… + 1/98 +1/99

Chứng tỏ rằng S > 1/2

 

 

 

Answer 1

;-;

Answer 2

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

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

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

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

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