If the sum to infinity of the series 1 + 4 x + 7 x 2 + 10 x 3 + . … … . is 35 16 , where x 1 , then x is equal to

Question

If the sum to infinity of the series 1 + 4 x + 7 x 2 + 10 x 3 + . … … . is 35 16 , where x 1 , then x is equal to, 19 7, 1 5, 1 4, 4 7

MARKS App · Accepted Answer

S = 1 + 4 x + 7 x 2 + 10 x 3 + . … … . x S = x + 4 x 2 + 7 x 3 + . … … . . On subtracting, we get, S 1 - x = 1 + 3 x + 3 x 2 + 3 x 3 + . … … . . = 1 + 3 x 1 1 - x , x 1 1 - x S = 1 - x + 3 x 1 - x = 1 + 2 x 1 - x S = 1 + 2 x 1 - x 2 = 35 16 (given) 16 + 32 x = 35 + 35 x 2 - 70 x ⇒ 35 x 2 - 102 x + 19 = 0 ⇒ 5 x - 1 7 x - 19 = 0 x = 1 5 , 19 7 But, x 1 ⇒ x = 1 5

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