Question

Chứng minh rằng :

                \(S=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}< 1\)

Answer 1

Ta có:

S = \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{19.20}=1-\dfrac{1}{20}< 1\)

Vậy S<1

Answer 2

Ta có:

S =

Vậy S<1

Answer 3

Ta có

Nên

Do đó 2S - S =

Answer 4

Ta có

Nên

Do đó 2S - S =