[" Let "x=1+a+a^(2)+..." and "y=1+b+b^(2)+...," where "|a|<1" and "|b|<1." Prove that "],[1+ab+a^(2)b^(2)+...=(xy)/(x+y-1)]

Let x = [(a + 2b)/(a+b)] " and " y = a/b , where a and b are positive integers . If y^2 gt 2 , then

If =1+a+a^(2)+oo, where |a|< 1andy =1+b+b^(2)+oo, where |b|<1 prove that: 1+ab+a^(2)b^(2)+oo=(xy)/(x+y-1)

If x=1 +a + a^2+…. to oo , where |a| lt1 and y=1+b+b^2+… to oo , where |b|lt1 , prove that 1+ab+a^2b^2+… to oo=((xy)/(x+y-1))

If x = 1+a+a^2+..........oo where abs(a)lt1 and y=1+b+b^2+........oo where abs(b)lt1 .Prove that 1+ab+a^2b^2+.......oo = (xy)/(x+y-1)

Let f(x) = ab sin x+ b sqrt( 1-a^2) cos x+c , where |a| lt 1, b gt 0 then

Let x=(a+2b)/(a+b) and y=(a)/(b) , where a and b are positive integers. If y^(2) gt 2 , then

Show that two lines a_(1) x + b_(14) y + c_(1) = 0 and a_(2) x + b_(2) y + c_(2) = 0 , where b_(1) , b_(2) ne 0 are Perpendicular if a_(1) a_(2) + b_(1) b_(2) =0 .

Show that two lines a_(1) x + b_(14) y + c_(1) = 0 and a_(2) x + b_(2) y + c_(2) = 0 , where b_(1) , b_(2) ne 0 are (i) Parallel if (a_1)/( b_1) = (a_2)/( b_2) and

Let A = [{:(2, b,1),(b, b^(2)+1,b),(1, b,2):}], " where "b gt 0 . Then, the maximum value of ("det"(A))/(b) is