Question

Exercitiul 3, va rog!
Vreau rezolvarea completa ca sa inteleg si eu cum se rezolva.

Answer 1

1/1+2=1/(2*3/2)=2/2*3
1/1+2+3=1/(3*4/2)=2/3*4
............................................
1/1+2+3+....+x=1/[x*(x+1)/2]=1*2/x*(x+1)=2/x(x+1)

2/2*3+2/3*4+......+2/x(x+1)=2[1/2*3+1/3*4+......1/x(x+1)]

Acum se foloseste faptul ca fiecare fractie se scrie in felul urmator
1/2*3=3-2/2*3=3/2*3-2/2*3=1/2-1/3
1/3*4=1/3-1/4
.......................
1/x*(x+1)=1/x-1/x+1
Cand le adun se va scrie asa
1+1/2-1/3+1/3-1/4+1/4-1/5+.......+1/x-1-1/x+1/x-1/(x+1)= 3/2-1/(x+1)=200/101
se aduce la ac numitor care este 202(x+1)
3*101(x+1)-2*101=400(x+1)
303x+303-202=400x+400
101-400=97x
-299=97x
x=-299/97