Question

o problema rezolvata cu inductia matematica,ofer 30 de puncte daca e corecta

Answer 1

p(n): 1/1*2+1/2*3+...+1/n(n+1)=n/n+1
I Verificare:
p1: 1/1*2=1/1+1
II Presupune P(k) adev. Arat P(k)=>P(k+1)
P(k): 1/1*2+1/2*3+...+1/k(k+1)=k/k+1
P(k+1): 1/1*2+1/2*3+...+1/(k+1)(k+2)=k+1/k+2
1/1*2+1/2*3+...+1/k(k+1)=k/k+1 /+ 1/(k+1)(k+2)
P(k+1): 1/1*2+1/2*3+...+1/(k+1)(k+2)=k/k+1+1/(k+1)(k+2)
.
.
.
.=> 1/1*2+1/2*3+...+1/(k+1)(k+2)=k+1/k+2 cf PIM P(n) adev.