Question

Numerele A1,A2,A3,....,An sunt invers proportionale cu numerele 2,6,12....,n(n+1).Daca A1+A2+A3+....+An=5400 si An-1-An=60,aflati n si An

Answer 1

2a1 = 6a2 = 12a3 =................=.n(n+1)an                                                   

a2 = a1/3 ; a3 = 1/2.3 ×a1;  a4 = 1/3.4×a1.......... an = 1/n(n+1)

a(n-1) - an = 1/n(n-1) - 1/n(n+1)=(n+1 -n +1)/n(n² -1) =2/ n(n²-1) =60

⇒   1/n(n-1)(n+1) = 60 ⇒   n(n-1)(n+1) = 1/ 3.4.5 ⇒n=3   

a1 + 1/1.3×a1 + 1 /2.3×a1 =5400 ⇒   a 1(1+ 1/3 + 1/6) =a1×3/2 = 5400 ⇒                     a1 = 5400×2/3 = 3600       a3 =3600/6 = 600