Question

Aflati ca numarul N=1+3+5+7…+999 este patratul unui numar natural

Answer 1

N = 1 + 3 + 5 + 7 + ...... + 999

( 999 - 1 ) : 2 + 1 = 998 : 2 + 1 = 499 + 1 = 500 termeni are suma

N = 500 × ( 1 + 999 ) : 2

N = 500 × 1 000 : 2

N = 500 × 500

N = 500²  → patrat perfect

N → este patratul numarului 500

Answer 2

N = 1 + 3 + 5 + 7 + ... + 999

N = 2×1-1 + 2×2-1 + 2×3-1 + 2×4-1 +...+ 2×500-1

N = 2 × (1 + 2 + 3 + 4 + ...+ 500) - (1 +1 +1...+ 1) de 500 de ori

N = 2 × 500 × (500 + 1) : 2 - 1 × 500

N = 500 × 501 - 500

N = 500 × ( 501 - 1)

N = 500 × 500

N = 500^2 p.p
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