Вправа 401 - 500 » 462

462. Скоротіть дріб (n — ціле число): a) (4^(n+2)- 4^n)/15 = (4^n (4^2- 1))/15 = (4^n •15)/15 = 4n; б) (5^(n+1)+5^(n+3))/26 = (5^(n+1) (1+ 5^2))/26 = (5^(n+1) •26)/26 = 5n+1; в) (3^n+ 1)/(3^(-n)+ 1) = (3^n+ 1)/(1+1) = (〖(3〗^n+ 1)3^n)/〖1+3〗^n = 3n; г) (6^(-n)+ 6^n)/(36^n+ 1) = (6^(-n) (〖1+6〗^2n))/(36^n+ 1) = 〖1+36〗^n/(6^n (36^n+ 1)) = 1/6^n .