Question

Chứng minh rắng S =1/2+1/2^2+1/2^3+...+1/2^20<1

Answer 1

S=1/2+1/2^2+1/2^3+...+1/2^20

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

=>2S-S=(1+1/2+1/2^2+...+1/2^19)-(1/2+1/2^2+1/2^3+...+1/2^20)

S=1-1/2^20<1

=>S<1

Vậy S<1