Question

Sa se arate ca numarul x este patrat perfect

X= 1+3+5+...+201
X=1004+2+4+6+...+2006​

Answer 1

Răspuns:

Explicație pas cu pas:

X= 1+3+5+...+201

suma are 101 termeni

X = 101*(1 + 201)/2 = 101*202/2 = 101*101 = patrat perfect

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2+4+6+...+2006​

suma are 1003 termeniS = 1003*(2 + 2006)/2 = 1003*2008/2 = 1003*1004

X = 1004 + 1003*1004 = 1004*(1 + 1003) = 1004*1004 = patrat perfect