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The coefficient of x9 in the expansion of (1 + x) (1 + x2) (1 + x3) ….. (1 + x100) is
Correct answer is '8'. Can you explain this answer?
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The coefficient of x9 in the expansion of (1 + x) (1 + x2) (1 + x3) &h...
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The coefficient of x9 in the expansion of (1 + x) (1 + x2) (1 + x3) &h...
We can expand the given expression using the distributive property:
(1 - x)(1 - x^2)(1 - x^3) = 1 - x - x^2 + x^3 - x^2 + x^3 + x^4 - x^5 - x^3 + x^4 + x^5 - x^6 - x^4 + x^5 + x^6 - x^7 - x^5 + x^6 + x^7 + x^6 - x^7 - x^8 + x^9
Simplifying this expression by combining like terms, we get:
1 - x - 2x^2 + 2x^3 + x^4 - 2x^5 - x^6 + 2x^7 + x^8 - x^9
Therefore, the coefficient of x^9 is -1.
(1 - x)(1 - x^2)(1 - x^3) = 1 - x - x^2 + x^3 - x^2 + x^3 + x^4 - x^5 - x^3 + x^4 + x^5 - x^6 - x^4 + x^5 + x^6 - x^7 - x^5 + x^6 + x^7 + x^6 - x^7 - x^8 + x^9
Simplifying this expression by combining like terms, we get:
1 - x - 2x^2 + 2x^3 + x^4 - 2x^5 - x^6 + 2x^7 + x^8 - x^9
Therefore, the coefficient of x^9 is -1.
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The coefficient of x9 in the expansion of (1 + x) (1 + x2) (1 + x3) ….. (1 + x100) isCorrect answer is '8'. Can you explain this answer?
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