Let `x=1+a+a^2+...` and `y=1+b+b^2+...` , where `|a|<1` and `|b|<1` . Prove that `1+a b+a^2b^2+...=(x y)/(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 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 x=(a+2b)/(a+b) and y=(a)/(b) , where a and b are positive integers. If y^(2) gt 2 , then

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

Let x_1, x_2, ,x_n be x_n observations. Let y_i=a x_i+b for i=1,2,...,n where a and b are constants. If the mean of x_i's is 48 and their standard deviation is 12, the mean of y_i 's is 55 and standard deviation of y_i's is 15, the values of a and b are (a) a=1. 25 ,b=-5 (b) a=-1. 25 ,b=5 (c) a=2. 5 ,b=-5 (d) a=2. 5 ,b=5

Let x_1, x_2, ,x_n be x_n observations. Let y_i=a x_i+b for i=1,2,...,n where a and b are constants. If the mean of x_i's is 48 and their standard deviation is 12, the mean of y_i 's is 55 and standard deviation of y_i's is 15, the values of a and b are (a) a=1. 25 ,b=-5 (b) a=-1. 25 ,b=5 (c) a=2. 5 ,b=-5 (d) a=2. 5 ,b=5