" 8.If "b=a+a^(2)+a^(3)+.......oo" prove that "a=(b)/(1+b)

If b=a+a^(2)+a^(3)+dot oo prove that a=(b)/(1+b)

If b = a+a^2+a^3+..... oo , lal lt1 .Prove that a=b/(1+b)

If b=a+a^2+a^3+ dotoo prove that a=b/(1+bdot)

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

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).

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 "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 "x=1+a+a^(2)+...oo,|a|lt1,y=1+b+b^(2)+...oo,|b|lt1,"then prove that ":(xy)/(x+y-1)=1+ab+a^(2)b^(2)+...oo

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)