Răspuns:
Explicație pas cu pas:
a)
2 + 4 + 6 + .....+ 200 = 2*(1 + 2 + 3 + ....+ 100)
fractia devine
(1 + 2 + 3 + ....+ 100)/2*(1 + 2 + 3 + ....+ 100) = 1/2
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b)
101 + 102 + 103 + .... + 200
=100 + 1 + 100 + 2 + 100 + 3 + .... + 100 + 100
=100*100 + 1 + 2 + 3 + .... + 100 = 100*100 + 100*(1 + 100)/2 =
= 100*100 + 50*101 = 10000 + 5050 = 15050
fractia devine
5050/15050 = 101/301
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c)
1 + 3 + 5 + .....+ 99 = 50*(1 + 99)/2 = 50*100/2 = 50*50
2 + 4 + 6 + ....+ 100 = 50*(2 + 100)/2 = 50*102/2 = 50*51
fractia devine
50*50/50*51 = 50/51
