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  • What is the sum of the coefficient of the term <img alt="\left ( \sqrt{2}-\sqrt[3]{3}+\sqrt[6]{5} \right )^{10}" src="https://learn.careers360.com/latex-image/?%5Cleft%20%28%20%5Csqrt%7B2%7D-%

What is the sum of the coefficient of the term \left ( \sqrt{2}-\sqrt[3]{3}+\sqrt[6]{5} \right )^{10}?

Option: 1

310


Option: 2

210


Option: 3

1


Option: 4

None of the above


Answers (1)

best_answer

 

 

Series Involving Binomial Coefficients -

In the expansion of (x + y + z)n if we put x = y = z  = 1, then we get the sum of coefficients. In this case, (1 + 1 + 1)n = 3n .  

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Sum of the coefficient (x_1+x_2+x_3)^n=(1+1+1)^n=3^n

To determine the coefficient 

Put x_1=1, \;x_2=-1,\;x_3=1\; and\;n=10

(1-1+1)^n=1^n=1

 

option C is correct.

 

Posted by

Shailly goel

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