What is the limit [n->inf] of summation [k=n to infinity] of (k-1)/k? Not sure since it's an infinite sum.

Question

I was initially thinking the answer was one, but the infinite sum is confusing me.

Answer 1

The sequence in question converges to one, as the previous answerer stated. However, it appears that this question is asking for the infinite sum, not where the infinite sequence converges. It's difficult to tell precisely though, because it's hard to read the expression without precise mathematical notation. However, if I am interpreting it correctly, than the infinite sum diverges. In order for an infinite sum to converge, the sequence in question must converge to 0. Since this sequence converges to 1, not 0, the infinite sum is divergent.

Answer 2

This is ifinity/infinity so use L'Hospital's rul
lim = 1/1 = 1