Răspunsuri

2014-10-26T11:40:54+02:00
1 + 3 + 5 + 7 + ... +999=1 + 3 + 5 + 7 + ... +(2*499+1)=(499+1)²=500²=250000 care este numar natural

am folosit formula=1+3+5+...+(2n+1)=(2n+1)²
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2014-10-26T11:46:15+02:00
Pentru fiecare exercitiu vom aplica formula de la 1+2+3+....+n =  \frac{n(n+1)}{2}
a )
1 + 3 + 5 + 7 + 9 + 11 = 1 + 2 + 3 + .... + 11 - 2 - 4 - .... - 10 = 1 + 2 +3 + ... + 11 - 2(1+2+...+5) =  \frac{11*12}{2} -  \frac{2*5*6}{2} = 11·6 - 30 = 66 - 30 = 36

b)
Aici vom face acelasi lucru ca la a :
N = 1 + 3 + 5 + .... + 999 = 1 + 2 + 3 + .... + 999 - 2 - 4 - 6 - .... - 998 = 1 + 2 + 3 + ... + 999 - 2(1+2+....+499) =  \frac{999*1000}{2} -  \frac{2*499*500}{2} = 999*500 - 499*500 = 500(999-499) =  500^{2}
4 4 4