Question

Sa se calculeze suma:
S=1/10+1/30+1/60+....+1/4950

Answer 1

Răspuns:

99/500

Explicație pas cu pas:

1/2*5+1/6*5+1/20*5+1/9900*5=

(1/5)*(1/1*2+1/2*3+1/3*4+....+1/99*100)=

=(1/5)*(1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100)=

(1/5) (1-1/100)=(1/5) *(99/100)=99/500