If `A=1+r^a+r^(2a)+` to `ooa n dB=1+r^b+r^(2b)+oo` , prove that `r=((A-1)/A)^(1//a)=((B-1)/B)^(1//a)`

If A=1+r^(a)+r^(2a)+ to oo andB=1+r^(b)+r^(2b)+oo, prove that r=((A-1)/(A))^(1/a)=((B-1)/(B))^(1/b)

If A=1+r^(2)+r^(2a)+...oo=a and B=1+r^(b)+r^(2b)+...oo=b then (a)/(b) is equal to

If R is a relation from A to B and S is a relation from B to C.Then prove that (SOR)^(-1)=R^(-1)OS^(-1)

Prove that : (r_1-r)/(a) +(r_2-r)/(b) = (c )/(r_3) .

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

Prove that : (r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)

If g_r is the r_(th) term of a G.P. with g_1=a nad g_2=b , then prove that sum_(r=1)^n g_1=(b.g_n-a^2)/(b-a)

If r_(1), r_(2) ,r_(3) are the ex-radii of DeltaABC, then prove that (bc)/(r_(1))+(ca)/(r _(2))+(ab)/(r _(3))=2R [((a)/(b)+(b)/a)+((b)/(c)+(c)/(b))+((c)/(a)+ (a)/(c))-3]

If x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))+...oo, and z=c+(c)/(r^(2))+(c)/(r^(4))+...oo prove that (xy)/(z)=(ab)/(c)

"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))-...oo,"and "z=c+(c)/(r^(2))+(c)/(r^(4))+...oo," then prove that "(xy)/(z)=(ab)/(c).