Odpowiedź:
an = (3n - 3)/(n + 1)
a(n + 1) = [3(n + 1) - 3]/(n + 1 + 1) = (3n + 3 - 3)/(n + 2) = 3n/(n + 2)
a(n+1) - an= 3n/(n+ 2) - (3n- 3)/(n + 1) =
= [3n(n + 1) - (n+2)(3n-3)]/[(n+ 2)(n+1)] =
= [3n² + 3n - (3n² + 6n - 3n - 6)]/[(n + 2)(n + 1)]=
= (3n²+ 3n - 3n² - 6n + 3n + 6)/[(n + 2)(n+1)] =
= 6/[(n+ 2)(n+1) = 6/(n²+2n+n+ 2) = 6/(n²+3n +2)
