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

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

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

If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo, prove that (x y)/z=(a b)/c

If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+oo, prove that (x y)/z=(a b)/c

If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo, prove that (x y)/z=(a b)/c

For a , b in R prove that (|a+b|)/(1+|a+b|) le (|a|)/(1+|a|)+(|b|)/(1+|b|)

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

"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).

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 a=sum_(r=1)^oo 1/r^4 then sum_(r=1)^oo 1/((2r-1)^4)=