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Aratati ca urmatoarele numere sunt patrate perfecte. a)X=1+3+5+....+41 b) y=203+2+4+6+......+404

Răspuns :

Didi12342
a)
X = 1+3+5+...+41
Aflam cati termeni are suma:
(41 - 1) : 2 + 1 = 40:2+1 = 21
X = (1+41) × 21 : 2
X = 42 × 21 : 2
X = 21 × 21
X = 21^2 patrat perfect

b)
Y = 203 + 2 + 4 + 6 +...+ 404
Y = 203 + 2 × (1 + 2 + 3 +..+202)
Y = 203 + 2 × 202 × 203 : 2
Y = 203 + 202 × 203
Y = 203 × (1 + 202)
Y = 203 × 203
Y = 203^2 p.p.

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