Răspuns:
Explicație pas cu pas:
a=1/1×2+1/2×3+1/3×4+......+1/49×50
1/1×2=1/1-1/2
1/2×3=1/2-1/3
1/3×4=1/3-1/4
1/49×50=1/49-1/50
.......................................
a=1-1/50=(50-1)/50=49/50
b) se face la fel 1/50×51=1/50-1/51 1/99×100=1/99-1/100
b=1/50-1/100=(2-1)/100=1/100
c)
1=(2k+1)A+(2k+3)B
k=-1/2 1=(-1+3)B B=1/2
k=-3/2 1=(-3+1) A A=-1/2
2/1×3=-1/1+1/3
2/3×5=-1/3+1/5
..........................
2/23×25=-1/23+1/25
c=1/25-1=-24/25