Question

Am nevoie de ajutor la acest egzercitiu!!!!!

Answer 1

Răspuns

a) verificare n=1⇒ 1=1(1+1)/2 -adevarat

presupunem p(k) =k(k+1)/2 adevarata si demonstram ca este si p(k+1) adevarata

p(k+1)=(k+1)(k+2)/2

1+2+3+....k+(k+1)=(k+1)(k+2)/2 adica

k(k+1)/2+(k+1)=(k+1)(k+2)/2⇔k(k+1)+2(k+1)=(k+1)(k+2)

(k+1)(k+2)=(k+1)(k+2) adevarat

b) verificare  n=1 ⇒1/3=1/2+1 adevata

presupunem p(k) =k/2k+1 adevarata si demonstram ca este si p(k+1) adevarata

1/1x3+1/3x5+....+1/(2k-1)(2k+1)+1/(2k+1)(2k+3)=(k+1)/(2k+3)

k/(2k+1)+1/(2k+1)(2k+3)=(k+1)/(2k+3)

aduci la acelasi numitor si va rezulta egalitatea

Explicație pas cu pas: