Question

Ultimile doua exerciții

Answer 1

Răspuns:

Explicație pas cu pas:

a)1/3+1/3²+1/3³+1/3^4+1/3^5+1/3^6 progresie geometrica cu ratia q=1/3

S=1/3·(1/64-1)/(1/3-1)=1/3(64-1)/64·3/2=63/128

b)1/2(1+1/2+1/4+1/8+1/16+1/32) progresie geometrica cu ratia q=1/2

S=1/2x1x(1/32-1)/(1/2-1)=1/2·(32-1)/32·2/1=31/32

5a)

1/3+5/18+2/9+4/27 (numitor comun=54)

=(18+5x3+2×6+4×3)/54=(18+15+12+12)/54=57/54

b)3/20+47/180+4/15+7/60 (numitor comun=180)

=(3x6+47+4x12+7x3)/180=134/180

c) 3/25+7/60+11/50+13/100 (numitor comun=300)

(3×12+7×5+11x6+13x3)/300=(36+35+66+39)/300=176/300