Question

1/2•3+1/3•4+...+1/(n-1)•n=2/5


Va rog rezolvarea completa!!!

Answer 1

Aplicam formula de calcul
1/k(k+1)=1/k -1 /k+1
Inlocuim pe k cu valori de la 2 pana la n-1 si obtinem ca
1 /2·3 +1 /3·4 +1 /4·5 +...+1 /(n-1)n=2/5 ⇔
1/2-1/3+1/3-1/4+1/4-1/5+...+1/n+1-1/n=2/5 ⇔
1/2-1/n=2/5 ⇔
n-2 /2n=2/5 ⇒4n=5n-10 ⇒n=10 ;