easy geometric series
Theorem.
n - 1 ----- i n ) 2 = 2 - 1 ----- i = 0
Proof.
Clearly, this is a geometric series, but one can also use the power of induction. For n=1, the statement is trivially states
0 1 2 = 2 - 1
Let’s suppose our theorem holds for every number below n>1. What about n itself?
n n - 1 / \ ----- i n ----- i n | n | n + 1 ) 2 = 2 + ) 2 = 2 + | 2 - 1 | = 2 - 1 ----- ----- \ / i = 0 i = 0
QuED…
