Răspuns:
1/2^10
Explicație pas cu pas:
Metoda 1:
1/2 - 1/4 - 1/8 - 1/16 - ... - 1/2^10 =
1/4 - 1(8 - 1/16 - ... - 1/2^10 =
1/8 - 1/16 - ... - 1/2^10 =
s.a.m.d..... se calculeaza primii doi termeni...
in final ajungem la
1/2^9 - 1/2^10 = 2-1 / 2^10 =
1/2^10.
Metoda a 2-a:
In paranteza avem suma S a n = 9 termeni consecutivi dintr-o progresie geometrica de ratie q = 1/2 si primul termen a1 = 1/2^2
S = a1(1-q^n)(1-q) = (1/2^2) x (1-1/2^9)/(1-1/2) = (1 - 1/2^9)/2
si astfel avem
1/2 -S = 1/2 - 1/2 + 1/2^10 =
1/2^10.
