Quandaries
and Queries 

Question: Can you please help me with a general formula for the following system: 2+2=2*2 3+3/2=3*3/2 4+4/3=4*4/3 and how will you prove the formula? 

Hi Tor, This question illustrates the usefulness of the algebraic idea of using letters to stand for numbers. If you rewrite the first equation as
you can see the pattern (equation) and put it into words.
It is certainly easier to write this equation using symbols. Let n be an integer, greater than 1. Can you prove the following equation is valid?
The right side can be written ^{(n n)}/_{(n  1)} but for the left side you need a common denominator
Hence the left side and right side of
are each equal to ^{(n n)}/_{(n  1)} and thus the equation
is valid. Penny 

