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If n is not a multiple of 3, then the co-efficient of xn in the expansion of loge (1 + x + x2) is
- a)-1/2
- b)-1/n
- c)2/n
- d)1/n
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If n is not a multiple of 3, then the co-efficient of xn in the expans...
Since n is not a multiple of 3.
∴ co-efficient of xn in first bracket = 0
as all powers of x are multiple of 3
also co-efficient of xn in second bracket
=1/n
Hence, required co-efficient = 1/n
∴ co-efficient of xn in first bracket = 0
as all powers of x are multiple of 3
also co-efficient of xn in second bracket
=1/n
Hence, required co-efficient = 1/n
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Community Answer
If n is not a multiple of 3, then the co-efficient of xn in the expans...
Explanation:
Given:
- n is not a multiple of 3
- Coefficient of xn in the expansion of loge (1 + x + x^2)
Expansion of loge (1 + x + x^2):
- We know that loge (1 + x) = x - x^2/2 + x^3/3 - ...
- Therefore, loge (1 + x + x^2) = (x - x^2/2 + x^3/3 - ...) + (x^2 - x^4/2 + x^6/3 - ...)
- Simplifying, we get loge (1 + x + x^2) = x + x^2/2 + x^3/3 + ...
Coefficient of xn:
- In the expansion of loge (1 + x + x^2), the term xn is present in the term x^n/n
- Therefore, the coefficient of xn is 1/n
Conclusion:
- The co-efficient of xn in the expansion of loge (1 + x + x^2) is 1/n, which corresponds to option 'D'.
Given:
- n is not a multiple of 3
- Coefficient of xn in the expansion of loge (1 + x + x^2)
Expansion of loge (1 + x + x^2):
- We know that loge (1 + x) = x - x^2/2 + x^3/3 - ...
- Therefore, loge (1 + x + x^2) = (x - x^2/2 + x^3/3 - ...) + (x^2 - x^4/2 + x^6/3 - ...)
- Simplifying, we get loge (1 + x + x^2) = x + x^2/2 + x^3/3 + ...
Coefficient of xn:
- In the expansion of loge (1 + x + x^2), the term xn is present in the term x^n/n
- Therefore, the coefficient of xn is 1/n
Conclusion:
- The co-efficient of xn in the expansion of loge (1 + x + x^2) is 1/n, which corresponds to option 'D'.
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If n is not a multiple of 3, then the co-efficient of xn in the expansion of loge (1 + x + x2) isa)-1/2b)-1/nc)2/nd)1/nCorrect answer is option 'D'. Can you explain this answer?
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