How do I check in maple if a series, is convergent or divergegent?

f:=((n-1)/2)/(1+((n-1)/2)^2);

is this function convergent or divergegent, and is it posible to decide only for odd n?

how to solve this eq by maple:

P:=Matrix([[ 0 , .5 , .5 , 0 , 0 , 0 ], [ 1/3 , 0 , 0 , 1/3 , 1/3 , 0 ], [ 1/3 , 0 , 0 , 0 , 1/3 , 1/3 ], [ 0 , 1 , 0 , 0 , 0 , 0 ], [ 0 , .5 , .5 , 0 , 0 , 0 ], [ 0 , 0 , 1 , 0 , 0 , 0 ]]);

pii:=Vector[row]([ a , b , c , d , e , f ])

how to find

pii.P=pii

Silaws