Question

F(x)=x+2
Sa se calculeze suma f(3)+f(3^2)+...+f(3^5)

Answer 1

f(3)=3+2
f(3^2)=3^2+2 
..
f(3^5)=3^5+2 ->>>
Adunam tot ->>>
f(3)+f(3^2)+...+f(3^5)=3+3^2+....3^5 +2+2+2+2+2
=2*5+3+3^2+3^3+..3^5
=10+ 3(3^5-1)/3-1=
=10+3^6-3/2
=20+729-3/2
=746/2
=373
Pt 3+3^2+..3^5 ->Folosim Sn.avand progresie geometrica ->S5