In the infinite series: 1 + 3 + 3 + 3 + 5 + 5 + 5 + 5 + 5 + 7 + ... each positive odd integer k appears k times in consecutive order.

1) Write a general formula that can be used to find the n_th term of the series.

2) Prove that if n is not 3, then the n_th partial sum of the series is never prime.

S(n) = (1/3)(2[v(n)] + 1)(3n - [(Vn)]^2 - [Vn)])

Edited on August 17, 2023, 7:58 am

Posted by K Sengupta on 2023-08-17 07:58:08