Question

Cho S = 1/11 + 1/12 + 1/13 + ... + 1/20

So sánh S với 1/2

CÁC BN GIÚP MIK NHOA

Answer 1

Mỗi phân số \(\frac{1}{11},\frac{1}{12},\frac{1}{13},...,\frac{1}{19}\)đều lớn hơn \(\frac{1}{20}\)

Do đó,\(S>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}(\)10 dãy \()\)

\(\Rightarrow S>\frac{10}{20}=\frac{1}{2}\)

Vậy \(S>\frac{1}{2}\)

Answer 2

\(\frac{1}{11}>\frac{1}{20}\)

\(\frac{1}{12}>\frac{1}{20}\)

\(⋮\)

\(\frac{1}{20}=\frac{1}{20}\)

Suy ra \(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}=\frac{10}{20}=\frac{1}{2}\)(có 10 số \(\frac{1}{20}\))

Answer 3

\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\) (10 số hạng

\(S< \frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)(10 số hạng

\(S< \frac{1}{20}.10\)

\(S< \frac{1}{2}\)

Answer 4

\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)

\(S< \frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)

\(S< \frac{1}{20}.10=\frac{1}{2}\)