The nth term of a series is given by `t_n = (n^5 + n^5)/(n^4 + n^2 + 1)` and if sum of its n terms can be expressed as `s_n = a_n^2 + a + 1/(b_n^2 + b)` , where `a_n` and `b_n` are the nth terms of some arithmetic progression and a, b are some constants , then prove that `b_n/a_n` is a constant.