Question

1+3+5+7+....+55=
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Multumesc.

Answer 1

1+3+5+7+...+55=
=1+2+3+4+5+6+7+...+54+55-(2+4+6+...+54)=
=55×56:2-2×(1+2+3+...+27)=
=55×28-2×27×28:2=
=28×(55-27)=28×28=784

Answer 2

Avem 2 variante de a calcula :

Varianta 1

1 + 3 + ... (2n - 1) = n²

2n - 1 = 55 => 2n = 56 => n = 28

1 + 3 + .. + 55 = 28² = 784

Varianta 2

1 = 2*0 + 1

3 = 2*1 + 1

..................

55 = 2*27 + 1

Suma devine

2*0 + 1 + 2*1 + 1 + ... + 2*27 + 1

Dam factor comun pe 2

2(1 + 2 + ... + 27) + 1*28 =

= 2*27*28 : 2 + 28

= 27*28 + 28

= 28(27 + 1)

= 28*28

= 28²

= 784