Question

Chứng minh rằng :

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

Answer 1

Ta có: S = 1/ 2 + 1/ 2^2 + 1/ 2^3 + ... + 1/ 2^20

Nên 2S = 1 + 1/2 + 1 / 2^2 + 1/ 2^3 + .... + 1/ 2^19

Do đó 2S - S = 1 - 1/ 2^20 < 1 

Vậy S < 1

Answer 2

2S=\(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{19}}\)

2S-S=1-\(\frac{1}{2^{20}}\)

S=\(1-\frac{1}{2^{20}}<1\)

S<1