does the series (1-(2/k))^k from k=1 to infinity converge?
you would get
(1-2)^1 + (1-1)^2 + (1 - 2/3)^3 + (1-2/4)^4 + (1-2/5)^5 + .... (1 - 2/100)^100 + ...
= -1 + 0 + 1/27 + 1/16 + 243/3125 + ... (49/50)^100 + ...
notice that the terms are actually increasing and as k becomes larger, the terms approach 1
so the sum becomes infinitely large
No, it does not converge, it diverges.