Question

So sánh tổng S= 1/5 +1/9+1/10+1/41+1/42

với 1/2

Answer 1

Ta có : \(\dfrac{1}{9}+\dfrac{1}{10}< \dfrac{1}{8}+\dfrac{1}{8}=\dfrac{1}{4}\)

\(\dfrac{1}{41}+\dfrac{1}{42}< \dfrac{1}{40}+\dfrac{1}{40}=\dfrac{1}{20}\)

\(\Rightarrow S=\dfrac{1}{5}+\dfrac{1}{8}+\dfrac{1}{9}+\dfrac{1}{41}+\dfrac{1}{42}< \dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{20}=\dfrac{1}{2}\) (đpcm)

Answer 2

1 9 + 1 10 < 1 8 + 1 8 = 1 4 và 1 41 + 1 42 < 1 40 + 1 40 = 1 20 Suy ra S = 1 5 + 1 9 + 1 10 + 1 41 + 1 42 < 1 5 + 1 4 + 1 20 = 4 5 1 20 + + = 1 2