Răspuns:
Explicație pas cu pas:
2/3*5 = 1/3 - 1/5
2/5*7 = 1/5 - 1/7
S = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + .... + 1/31 - 1/33
= 1/3 - 1/33 = 11/33 - 1/33 = 10/33
S= 2/3x5+2/5x7+2/7x9+.....+2/31x33
observam ca putem scrie scriem 2/3×5=1/3-1/5
pe 2/5x7=1/5-1/7
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2/31x33=1/31-1/33
acum inlocuim in S
S=1/3-1/5+1/5-1/7+....+1/31-1/33
si observam ca se reduc termenii ramanand doar 1/3-1/33
deci S=1/3-1/33= (33-3)/(3×33)=30/99=10/33
