Divergent Series

If you tour around bookstores or pay attention to the movies... you will see nowadays kids read the Divergent series. Kids have strong demand of good reading materials... They yearn for it. This sure is encouraging for novelists. Now I don't have a clue what this is about other than it must be some teenage heroes and heroines saving the day somehow. (Isn't that an element of just about every story?)

Some teenagers may also encounter a different type of divergent series... You guessed it. A series of numbers when you add them up do not total to a specific number. It "escapes to infinity" as some say. Excellent coverage right on wikipedia: here. (and I actually understand so little of that to be honest)

Now just why the heck do we care of a series converges or diverges. One reason is this: so you can make some use of calculus 101. See here. I find this the least interesting topic of calculus. Yes, you don't need this in "real-life".

But it IS interesting that the harmonic series: 1 + 1/2 + 1/3 + 1/4 +... diverges. Each number gets smaller of course but this is not coming down fast enough to converge as in 1 + 1/2 + 1/4 + 1/8 + ... And in the old days people don't actually have computers that you can write a little summation loop to verify yourself. Here do a little for loop and add 100 items to see for yourself.