Răspuns
suma se mai scrie
S=(1/2+1/2³+...+1/2¹⁹)-(1/2²+1/2⁴+....+1/2²⁰)
In prima paranteza ai o progresie geometrtica cu 10 termeni si ratia 1/4
S1=(1/2+...+1/2¹⁹)=1/2*[(1/4)¹⁰-1]/(1-1/4)=1/2*[(1/4)¹⁰-1]/(3/4)=
2[(1/4)¹⁰-1]/3 (A
In a 2 a paranteza ai o progresie geometrica cu 10 termeni si ratia 1/2²=1/4
S2=(1/2²+...+1/2²⁰)=1/4*[(1/4)¹⁰-1]/(1-1/4)=1/4*[(1/4)¹⁰-1]/(3/4)=[(1/4)¹⁰-1]/3 (B
S=S1-S2=
2[(1/4)¹⁰-1]/3-[(1/4)¹⁰-1]/3=
[2(1/4)¹⁰-2-(1/4)¹⁰+1]/3=
[(1/4)¹⁰-1]/3
Explicație pas cu pas:
