Răspuns:
Explicație pas cu pas:
f(3)=3+2
f(3²)=3²+2
f(3³)=3³+2
......................
f(3¹⁵)=3¹⁵+2
Le adui
f(3)+f(3^2)+f(3^3)+...+f(3^15)=(3+3^2+3^3+...+3^15)+(2+2+...+2)=
Prima paranteza reprezinta o progresie geometrica de ratie 3 , determini suma acesteia cu formula
Sn=a1*[q^n-1]/[q-1] unde a1=3, n=15, q=3
S15=3*(3^15-1)/(3-1)=3^16-3)/2
In paranteza a 2-a avem o suma cu 15 termenii egali cu 2=>
f(3)+...f(3^15)=(3^16-3)/2+15*2
