Question

Va rog ajutati-ma la punctele: c,d,e...
va rog din suflet, ca am nevoie ​

Answer 1

Răspuns:

P(m):1+5+9+...+(4n-3)=n(2n-1);neN

1)P(1): 1=1(2-1)

1=1 (A)

P(k): 1+5+9+...+(4k-3)=k (2k-1)

P (k+1):1+5+9+...+(4k-3) + (4k+1)= (k+1) (2k+1)

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

2k^2-k+4k+1=2k^2+k+2k+1

2k^2+3k+1=2k^2+3k+1-"A"=>P(k)-"A"=>P(n)-"A"