Don’t ask my why, I’m going to guess the limit of this series = e-2 = 0.7182818284590452353602874713526624977572470936

I admittedly have no proof of this. I simply started looking at n=1 through n=101. After the first couple (around n=5), I simply noticed that the sum was growing, not decreasing to 0 as I had said in a previous comment. Then things started to slow down around 0.68 through 0.69. I got tired of looking and thought, "isn’t there a special number that is 0.71 or something?" I confirmed what e was, and just took a guess.

Like I said, no proof, so any attacks to disprove my lack of proof will not affect me.