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

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 +