Question

1+5+9+. +(4n-3)=n(2n-1).

Answer 1

Membrul stang:

1 + 5 + 9 + ..... + (4n - 3) = ?

Nr termeni = [(4n - 3) - 1] : 4 + 1

Nr termeni = (4n - 4) : 4 + 1

Nr termeni = n - 1 + 1

Nr termeni = n

Suma = [(4n - 3) + 1] * n / 2

Suma = (4n - 2)/2  * n

Suma = (2n - 1) * n

Membrul stang = membrul drept

n * (2n - 1) = n * (2n - 1)

Adevarat