Consider the sequence a_k=√(k+1)-√(k)= 1/√(k+1)+√(k) and the infinite series [infinity]∑ k=1 aₖ. Which of the following is true?
(A) lim (k→[infinity]) aₖ=0 and [infinity]∑ k=1 aₖ converges.
(B) lim (k→[infinity]) aₖ≠0 and [infinity]∑ k=1 aₖ converges.
(C) lim (k→[infinity]) aₖ=0 and [infinity]∑ k=1 aₖ diverges.
(D) lim (k→[infinity]) aₖ≠0 and [infinity]∑ k=1 aₖ diverges.

O A
O B
O C
O D