If the number of terms in the expansion of , x 0, is 28, then the sum of the coefficients of all the terms in this expansion, is

Engineering

Mathematics

Distribution of Alike Objects or Beggars Methods

Question

If the number of terms in the expansion of ${(1− \frac{2}{x} + \frac{4}{x^{2}})}^{n}$ , x $\neq$ 0, is 28, then the sum of the coefficients of all the terms in this expansion, is

243

2187

729

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Put x = 1

3ⁿ = sum of coefficient

Number of terms in ${(1 - \frac{2}{x} + \frac{4}{x^{2}})}^{n}$ is 28.]

2n + 1 = 28 (not possible).

Incorrect Solution:

Number of terms ⁿ⁺²C₂ = 28

n + 2 = 6 ⇒ n = 6

Put x = 1.

Sum: (1– 2 + 4)⁶ = 3⁶ = 729.