Let 
be a geometric sequence with quotient 
and first term 
. Let there be a sequence with the general term 
.
Write down the general term of the sequence and prove that the sequence 
is arithmetic with difference 
.
Calculate the sum of the first 100 terms of the sequence .
Prove that for any pair of natural numbers m, n, 
and 
are not odd numbers.
Let for every natural number n 
be a polynomial defined by the rule 
. Prove that for every natural number n the polynomial on the interval 
has exactly one zero.
