Question

So sánh: S=1/11+1/12+1/13+...+1/20 và  1/2 

Answer 1

SSH của S là: 

       (20-11):1+1=10(số).

Vì 1/11>1/20;1/12>1/20;...;1/19>1/20;1/20=1/20.

=>S>1/20+1/20+...+1/20(10 số 1/20).

=>S>1/20*10.

=>S>1/2.

Vậy S>1/2.

Answer 2

S=(1/11+1/12+1/13+1/14+1/15)+(1/16+1/17+1/18+1/19+1/20)

S>(1/15+1/15+1/15+1/15+1/15)+(1/20+1/20+1/20+1/20+1/20)

S>1/15x5+1/20x5

S>1/3+1/4

S>7/12>6/12=1/2

->S>1/2

Answer 3

Số số hạng của S là:

    (20 - 11 ): 1 + 1 = 10 (số)

Ta thấy:

\(\frac{1}{11}>\frac{1}{20};\frac{1}{12}>\frac{1}{20};...;\frac{1}{19}>\frac{1}{20}\)

\(=>\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}\)\(>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}=\frac{10}{20}=\frac{1}{2}\)

\(=>S>\frac{1}{2}\)