a) SEQUENCE is a list of numbers in order.When we say one sequence is convergent, we have lim a_n (n approach to infinity) equals a defined number. For example, a_n=n/(n+1), lim a_n =1, 1 is the constant. when n becomes larger and larger, a_n can be as close as possible to 1, sequence {a_n} is convergent . When we say one sequence {a_n} is divergent, we can not define the exact value of a_n when n approaches infinity. a_n=n, lim a_n = ∞ . The difference between divergent and convergent sequence can be found out by proving the sequence formula that whether it is infinite or finite.
b)SERIES can seem as the sum of infinite terms of a sequence. To find whether it is convergent or divergent, it does not work if we just see whether the sequence converges or diverges. When we say a series is convergent, we have a sum of {a_n}(n approaches infinity) is bounded. Whatever how many terms you add up, the value of series can only locate in bounded intervals. Like an=1/(n^2), lim sum of {a_n}=log2, the value is bounded above log2. Or we have divergent series, we have a sum of {a_n}(n approaches infinity) is without limit. Like an=1/n, lim sum of {a_n}=∞, the value can be as large as possible with the increase of term.