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 = ∑ 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, x , y , z are in A.P., x , y , z are in G.P., 1 x , 1 y , 1 z are in A.P., 1 x + 1 y + 1 z = 1 - a + b + c

MARKS App · Accepted Answer

x = 1 + a + a 2 = . . . . . . x = 1 1 - a ⇒ a = 1 - 1 x y = 1 1 - b ⇒ b = 1 - 1 y z = 1 1 - c ⇒ c = 1 - 1 z a , b , c are in A.P. ⇒ 1 - 1 x , 1 - 1 y , 1 - 1 z are in A.P. ⇒ - 1 x , - 1 y , - 1 z are in A.P. ⇒ 1 x , 1 y , 1 z are in A.P.

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