Question

Cho S= \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\)

So sánh S với \(\frac{1}{2}\)

Answer 1

mình học toán cảm thấy nhức óc lắm, hoa mắt luôn

Answer 2

Ta thấy:

1/11<1/4

1/12<1/4

.......

1/20<1/4

Suy ra ta có:

$\frac{\mathrm{(1/}}{11}+\frac{\mathrm{1/}}{12}+\frac{\mathrm{1/}}{13}+\frac{\mathrm{1/}}{14}+\frac{\mathrm{1/}}{15}+\frac{\mathrm{1/}}{16}+\frac{\mathrm{1/}}{17}+\frac{\mathrm{1/}}{18}+\frac{\mathrm{1/}}{19}+\frac{\mathrm{1/}}{\mathrm{20)<1/4\; nhân\; 2\; hay\; chính\; là\; nhỏ\; hơn\; 1/2}}$

Answer 3

Vì \(\dfrac{1}{11}>\dfrac{1}{20};\dfrac{1}{12}>\dfrac{1}{20};....;\dfrac{1}{19}>\dfrac{1}{20};\dfrac{1}{20}=\dfrac{1}{20}\)

\(\Rightarrow s>\dfrac{1}{20}+\dfrac{1}{20}+\dfrac{1}{20}.........+\dfrac{1}{20}\)(20 phân số)

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

Vậy \(S>\dfrac{1}{2}\)