Răspuns:
1/3-1/3*2^21= (1/3) (1-1/2^21)
sau, altfel scris,
(2^21-1)/3*2^21
Explicație pas cu pas:
calculam
S=1-s=1-1/2+1/2²-1/2³+......-1/2^19+1/2^20= (1-(-1/2)^21)/(1-(-1/2)**=
(1+1/2^21)/(3/2)= (2/3)*(2^21+1)/2^21= 2(2^21+1)/3*2^21
s=1-S=1-(1-s)
s= 1- 2(2^21+1)/3*2^21=
=(3*2^21-2*2^21-1)/3*2^21=
=(2^21-1)/3*2^21= eventual 1/3-1/3*2^21= (1/3) (1-1/2^21)
**** S20 pt progresie geometrica, avand b1=1 si q=-1/2
