We consider a bijective map f: N→ N and the series f(n) n² b) Show that S= We want to show that there is no bijective map f such that the series S converges. To this end, we assume that the series converges. As all term in the series are positive, the series then converges absolutely and we may rearrange the contributions without altering the limit. a) Argue that n=1 f(1) + f(2)+...+ f(n) ≥ 1+...+n= n=1 n² n(n+1) 2 (n + 1)2 k² n=k and insert the identity in the series S. Then exchange the order of the summations to show that f(n) -((1) + f(2) + ... + f(n)) ((n + 1)²) 72² 1 (2 marks) 7=1 Hint: draw Nx N in a coordinate system and mark the points that contribute to the sum. Deduce how the sum looks from this drawing when you exchange the order of the sums. (5 marks) c) Deduce with the results from part a) and b) that the series S diverges.