Question

Sa se calculeze limitele sirurilor an=(1+1/4+...+1/4^n)(1+1/5+...+1/5^n)

Answer 1

(1+1/4+,,,+1/4^n=suma     unei     progresii   de    ratie 1/4 avand n+1    termeni=

[(1/4)^n-1]/(1/4-1)=[1/4)^n-1]/(-3/4)=4(1-(1/4)^n)/3→4/3    pt   ca (1/4)^n→0