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If (1+x)^7 then which one of the following is true?

Option: 1

The number of terms in the expansion is 8.


Option: 2

Value of the given expansion is 1+x if x=\omega, and \omega shows the cube root of unity


Option: 3

For every value of x, the first term of the expansion is unaltered.


Option: 4

All of the above.


Answers (1)

best_answer

A. Number of terms is equal to 7+1=8

 

B.

\\(1+x)^7=(1+\omega)^7=(-\omega^2)^7\\-\omega^{14}=-(\omega)^{14}=-(\omega)^{12}\cdot(\omega)^{2}=-\omega^2=1+\omega

 

C.

Expansion of 

 \\(1+x)^7=\sum_{r=0}^{n}\;^nC_{0}1^{n-r}x^r

for first term r=0

T_1=\;^nC_01=1

 

Hence all of the above is correct

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manish

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