Question

demonstrati ca 3+5+7+....+(2n+1)=m(n+2)
ajutati plssss

Answer 1

..............................................

Answer 2

3+5+7+....+(2n+1)=n(n+2)

se rezolva cu ajutorul sumelor Gauss

1 + 2 + 3 + .......+ n =[n (n+1)}:2

3 + 5 + 7 + ....+ (2n + 1)

= 1 + 2 + 3 +....+ (2n+1) + ( 2n +2) - 1 - 2 [1  + 2 + 3 +.....+n + (n + 1)]

= [(2n + 2)(2n + 3)]:2 -1 - 2[(n + 1)(n + 2)]:2

= (n + 1)(2n + 3) -1 - (n + 1) ( n + 2)

= ( n + 1)( 2n +3 -n - n) -1

= (n + 1)²-1

= n² +2n

= n(n+2)