In the known sequence {an}, A1 = 4, an = 3A (n-1) - 2 (n ≥ 2) (1) Prove: the sequence {an-1} is an equal ratio sequence, and find the general term of the sequence {an} (2) It is proved that 1 / A1 + 1 / A2 +... + 1 / an < 1 / 2

In the known sequence {an}, A1 = 4, an = 3A (n-1) - 2 (n ≥ 2) (1) Prove: the sequence {an-1} is an equal ratio sequence, and find the general term of the sequence {an} (2) It is proved that 1 / A1 + 1 / A2 +... + 1 / an < 1 / 2


(1)an=3a(n-1)-2an-1 = 3(a(n-1) -1)(an-1)/(a(n-1) -1)=3(an-1)/(a1-1) =3^(n-1)an = 1+ 3^n(2)1/an = 1/(1+3^n) < 1/3^n1/a1+1/a2+..1/an < 1/3 +1/3^2 +...+1/3^n= (1/3)(1- (1/3)^n )/ (1-1/3)= (1/2)(1- (1/3)^...

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