Need help! I'm computing for the general formula of this sequence $S = 1 + 4t^2 + 9t^4 + \ldots + n^2 t^{2n - 2}$. I tried multiplying the equation by $t^2$ then subtracting it by the original equation..I do this twice... but I only got few terms correct..
the correct answer based on an online calculator is $n^2 t^{2n} – 2n^2 t^{2n+2} + n^2 t^{2n+4} + 2nt^{2n} + t^{2n} – 2nt^{2n+2} + t^{2n+2} – t^2 - 1$.
How is this possible? I got $7$ terms correct...but nowhere to find the other $2$..I check my work over and over...but still nothing come up...