SUCCEED WITH MATH:
Every Student's Guide to Conquering Math Anxiety
Chapter 5. Taming Numbers
In this chapter we shall look more closely at how numbers behave.
You have probably heard children arguing that a trillion, trillion, trillion is the largest number, only to be topped by some very canny child who simply adds one or multiplies the last large number by two. This was precisely the puzzle that intrigued the Greeks. If every apparently last or largest number can be added on to or increased by multiplication, how will we ever get to the very largest, or the very last, number of all?
One pattern that reveals itself when you begin to sum integers is the so-called law of odd numbers. Take a sequence made up of odd integers beginning with 1: 1, 3, 5, 7, 9, 11. Add them and you will find that they sum to sequential squares:
1 + 3 = 4 (2 x 2)
1 + 3 + 5 = 9 (3 x 3)
1 + 3 + 5 + 7 = 16 (4 x 4)
1 + 3 + 5 + 7 + 9 = 25 (5 x 5)
This relationship was known before Galileo Galilei (1564-1642),
but he was the first to see that the sum of odd numbers corresponds
to the behavior of falling bodies...
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