Question

Sa se efectueze:
b) (1-1/2)+(1-5/6)+(1-11/12)+.....+(1-109/110)
c) (1-1/19)+(1-2/19)+(1-3/19)+.....+(1-19/19)
d) 50-1/25-2/25-3/25-......-25/25

Answer 1

c) aducem la acelasi numitor in fiecare paranteza
   (19/19-1/19)+(19/19-2/19)+(19/19-3/19)+.....+(19/19-19/19)=
    18/19+17/19+16/19+.....+1/19+0=
    1/19*(18+17+16+...+1)=1/19*18*19/2=9
d)50-1/25*(1+2+2+...+25)=
    50-1/25*25*26/2=50-26/2=50-13=37