The sum of the coefficients in the binomial expansion of ( 1 x + 2 x ) 6 is equal to

Question

The sum of the coefficients in the binomial expansion of ${(\frac{1}{x} + 2 x)}^{6}$ is equal to

Smart Achievers · Accepted Answer

(2)

${(\frac{1}{x} + 2 x)}^{6} = {}^{6}C_{0} {(\frac{1}{x})}^{6} {(2 x)}^{0} + {}^{6}C_{1} {(\frac{1}{x})}^{5} {(2 x)}^{1}$ $+ {}^{6}C_{2} {(\frac{1}{x})}^{4} {(2 x)}^{2} + {}^{6}C_{3} {(\frac{1}{x})}^{3} {(2 x)}^{3} + {}^{6}C_{4} {(\frac{1}{x})}^{2} {(2 x)}^{4}$ $+ {}^{6}C_{5} (\frac{1}{x}) {(2 x)}^{5} + {}^{6}C_{6} {(\frac{1}{x})}^{0} {(2 x)}^{6}$

$= {(\frac{1}{x})}^{6} + 12 {(\frac{1}{x})}^{4} + 60 {(\frac{1}{x})}^{2} + 160 + 240 x^{2} + 192 x^{4} + 64 x^{6}$

$Sum of coefficients = 1 + 12 + 60 + 160 + 240 + 192 + 64 = 729$

Solution

Q.
The sum of the coefficients in the binomial expansion of ${(\frac{1}{x} + 2 x)}^{6}$ is equal to

1 1024

2 729

3 243

4 512

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