Question

P(n) 1+2+3+...+2n=n(2n+1)
Ma puteti ajuta va rog cu p(n)A si dem p(n+1)

Answer 1

Inductie matematica completa:
Verificam pt n=1: 1+2=1(2+1)=3, se verifica.
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 PP adevarat pt n=k, adica P(k)=k(2k+1) adevarat si
vom demostra ca si pt n=k+1 avem adevar, adica P(k+1)=(k+1)(2k+3):
P(k+1)= P(k) + 2k+1 + 2k+2 = k(2k+1)+4k+3=2k^2+5k+3=2k^2+2k+3k+3=2k(k+1) + 3(k+1) = (k+1)(2k+3), deci adevar. C.c.t.d.