(.14*99500*4)+(660*12)+(275*2*12)

a=((1+p)/(1-q-q p))
b=((1-(p^2))/(q (p^2)))
Assuming[Element[{a,b},Reals]&&0≤ p≤1 && 0≤ q≤1 && p+q==1,Simplify[a-b]]

a/.{p->.7,q->.3}
b/.{p->.7,q->.3}

eq=a-b==0
eq2=p+q==1
Solve[{eq,eq2},{p,q}]

a-b//FullSimplify

SameQ[a,b]

?SameQ

SameQ[a-b,0]

mat={{0,1/m,0,1/m,0},{0,0,1/m,1/m,0},{0,0,0,1/m,0},{0,1/m,0,0,1/m},{0,1/m,0,0,0}};
MatrixForm[mat]
fundamentalMatrix=Inverse[IdentityMatrix[5]-mat];
MatrixForm[fundamentalMatrix]
s=Total[fundamentalMatrix[[1,1;;-1]]]//FullSimplify
Apart[%]
%/.{m->2,k->3}

s

Expand[s]

s/.{k->3,m->2}

f[k_,m_]:=Sum[m^i,{i,0,k-1}]
f[3,2]

6.3/6