Question

cum sa rezolv???????

Answer 1

2^a<2^(1/2)

cum 2^x estecrescatoare pe R, este suficient sa aratam ca a<1/2

a=1/3+1/9++...+1/3^n= (1/3) (1+1/3+1/3²+...+1/3^(n-1))=

(1/3)*(1-(1/3)^n):(1-1/3)=

=(1/3)*(3/2)* (1-(1/3)^n=

=(1/2) *(1-(1/3)^n)<1/2 pt ca (1-(1/3)^n)<1, ∀n∈N*