Răspuns:
Explicație pas cu pas:
b) Presupunem p(n) adevarata si
sa demonstram ca p(n+1) = (n+1)/(2(n+1) +1)
p(n+1) = 1/1*3 +1/3*5 +...+1/(2n-1)(2n+1) +1/(2n+1)(2n+3) =
=n/(2n+1) +1/(2n+1)(2n+3) = 1/(2n+1)(n + 1/(2n+3)) =
= 1/(2n+1)(2n^2 +3n +1)/(2n+3) =
= 1/(2n+1)(n+1)(2n+1)/(2n+3) =
= (n+1)/(2n+3) = (n+1)/(2(n+1) +1) = p(n+1)
c) Se rezolva similar
