It is known that the general term formula of sequence {an} is an = 8N (4n2 − 1) 2, and Sn is the sum of the first n terms. The values of S1, S2 and S3 are calculated. According to the calculation results, the formula for calculating SN is deduced and proved by mathematical induction
S1 = A1 = 89, S2 = a1 + A2 = 2425, S3 = S2 + a3 = 4849. Guess Sn = (2n + 1) 2 − 1 (2n + 1) 2. Prove: ① when n = 1, from the above, guess is true. ② suppose n = k, guess is true, that is SK = (2k + 1) 2 − 1 (2k + 1) 2. Then when n = K + 1, SK + 1 = SK + AK + 1 = (2k + 1) 2 − 1 (2k + 1) 2 +