Răspuns:
Explicație pas cu pas:
a)
1/1*2 = 1 - 1/2
1/2*3 = 1/2 - 1/3
.....
1/99*100 = 1/99 - 1/100
_______________
1/1*2 + 1/2*3 + ...+ 1/99*100 = 1 - 1/2 + 1/2 - 1/3 + ...+ 1/99 - 1/100 = 1 - 1/100 = 99/100 = 0,99
0,5 < 0,99 < 1 adevarat
___________________
b)
2/1*3 = 1 - 1/3
2/3*5 = 1/3 - 1/5
2/5*7 = 1/5 - 1/7
........
2/99*101 = 1/99 - 1/101
___________
2/1*3 + 2/3*5 + 2/5*7 + ...+ 2/99*101
= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ...+ 1/99 - 1/101
= 1 - 1/101 = 100/101
100/101 + 2/100*101 = 100*100/100*101 + 2/100*101 = 10002/ 10100 < 1
