examples to compare tradtional math notations vs APL/J notations [closed]

Question

I am reading a review to compare Mathematica to APL/J. One question raised in the article seems very interesting to me:

Is Mathematica really the way to go to express our creative thoughts – viz back to a 17th century notation designed for parchment instead of forward to a twentieth-century one designed for computers?

Can one share examples of Iverson's notation vs traditional math notation to demonstrate the edge of APL/J on expressing and solving math problems? This would be greatly helpful for new comers.

Answer 1

One example: Alternating series.

Alternating sum is very common in mathematics. But it is cumbersome to put the sign before each term:

in APL and J, because of the order of operations, it is

-/a