If the sum of the coefficients in the expansion of 1 + 3 x n lies between 4000 and 10000 , then the value of the greatest coefficient must be

Question

If the sum of the coefficients in the expansion of 1 + 3 x n lies between 4000 and 10000 , then the value of the greatest coefficient must be, 3954, 6342, 4806, 1458

MARKS App · Accepted Answer

Putting x = 1 to get the sum of the coefficients, we get, 4000 4 n 10000 ⇒ n = 6 4 5 = 2 10 = 1032 The greatest coefficient is the greatest term in the expansion of 1 + 3 x 6 when x = 1 . For 1 + 3 x 6 , m = 3 x 6 + 1 3 x + 1 = 3 × 7 4 = 5.25 ⇒ Greatest term is T m + 1 = T 5 + 1 = 6 C 5 3 x 5 = 6 × 3 5 × x 5 Greatest coefficient = 6 × 3 5 = 1458

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