Question

Arătați ca:n=1+2+3+..+(2n+1), este pătrat perfect​

Answer 1

Răspuns:

S=1+3+5+...+(2n-3)+(2n-1)+(2n+1)

2S=(2n+1)+(2n-1)+(2n-3)+...+5+3+1

2S=(2n+2)

2S=2·(n+1)·(n+1) |:2

S=(n+1)² patrat perfect

Answer 2

S = 1 + 3 + .. + 2n + (2n + 1)

S = (2n + 1) + 2n + .. + 3 + 1

adunam relatiile

2S = (2n + 2) + (2n + 2) + .. + (2n + 2) + (2n + 2)

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

2S = 2(n + 1)(n + 1)

2S = 2(n + 1)²

S = (n + 1)²