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S=2+4+6+...... ....+108

Răspuns :

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[tex]S = 2 + 4 + 6 + ... + 108[/tex]

[tex]S = 2(1 + 2 + 3 + ... + 54)[/tex]

[tex]S = 2 \times \frac{54(54 + 1)}{2} [/tex]

[tex]S = 54(54 + 1)[/tex]

[tex]S = 54 \times 55[/tex]

[tex]S = 2970[/tex]

[tex]Formul \check{a} \: : \: 1 + 2 + 3 + ... + n = \frac{n(n + 1)}{2} [/tex]

Folosim formula lui Gauss

1 + 2 + ... + n = n (n + 1) : 2

S = 2 + 4 + .. + 108

S = 2(1 + 2 + .. + 54)

S = 2(54*55 : 2)

S = 54*55

S = 2970

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