If the number of terms in the expansion of 1-2-x-4-x2n- x-0- is 28 - then the sum of the coefficients of all the terms in this expansion-is-

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Standard XI

Mathematics

Sum of binomial coefficients of odd numbered terms

If the number...

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

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729

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2187

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Solution

The correct option is B 729
$total number of terms =^{n + 2} C_{2} = 28 (n + 2) (n + 1) = 56 n = 6$
Sum of coefficients $= (1 - 2 + 4)^{n} = 3^{6} = 729$

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If the number of terms in the expansion of (1−2x+4x2)n, x≠0, is 28, then the sum of the coefficients of all the terms in this expansion,is:

The correct option is B 729total number of terms =n+2C2=28(n+2)(n+1)=56n=6 Sum of coefficients =(1−2+4)n=36=729

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:

The correct option is B 729
$total number of terms =^{n + 2} C_{2} = 28 (n + 2) (n + 1) = 56 n = 6$
Sum of coefficients $= (1 - 2 + 4)^{n} = 3^{6} = 729$