If x = ∑ n = 0 ∞ a n ,   y = ∑ n = 0 ∞ b n ,   z = ∑ n = 0 ∞ c n , where a , b , c are in A.P. and a < 1 , b < 1 , c < 1 , a b c ≠ 0 , then

Question

If x = &#8721; n = 0 &#8734; a n , &#160; y = &#8721; n = 0 &#8734; b n , &#160; z = &#8721; n = 0 &#8734; c n , where a , b , c are in A.P. and a &#60; 1 , b &#60; 1 , c &#60; 1 , a b c &#8800; 0 , then

Aicharya · Accepted Answer

x = 1 + a + a 2 = . . . . . . x = 1 1 - a &#8658; a = 1 - 1 x y = 1 1 - b &#8658; b = 1 - 1 y z = 1 1 - c &#8658; c = 1 - 1 z a , b , c are in A.P. &#8658; 1 - 1 x , 1 - 1 y , 1 - 1 z are in A.P. &#8658; - 1 x , - 1 y , - 1 z are in A.P. &#8658; 1 x , 1 y , 1 z are in A.P.

If x = ∑ n = 0 ∞ a n ,   y = ∑ n = 0 ∞ b n ,   z = ∑ n = 0 ∞ c…

Solution

If x = &#8721; n = 0 &#8734; a n , &#160; y = &#8721; n = 0 &#8734; b n , &#160; z = &#8721; n = 0 &#8734; c…

Solution

If x = ∑ n = 0 ∞ a n , y = ∑ n = 0 ∞ b n , z = ∑ n = 0 ∞ c…