Question

2+4+6+8+.........+2n=n² rezolvare va rog frumos

Answer 1

Răspuns:

2 + 4 + ... + 2n = n² + n

For n = 1, then :

2(1) = 1² + 1

2 = 1 + 1

2 = 2

PROVEN...

For n = k , then :

2 + 4 + ... + 2k = k² + k

TRUE

For n = k + 1, then :

2 + 4 + ... + 2k + 2k + 2 = (k + 1)² + (k + 1)

k² + k + 2k + 2 = (k + 1)² + (k + 1)

k² + 2k + 2 + k = (k + 1)² + (k + 1)

k² + 2k + 1 + k + 1 = (k + 1)² + (k + 1)

(k² + 2k + 1) + (k + 1) = (k + 1)² + (k + 1)

(k + 1)² + (k + 1) = (k + 1)² + (k + 1)

Explicație pas cu pas:

hope its good