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further work with coefficients binomial (1 Viewer)

Halo189

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The coefficients of x^4 and x^5 in the expansion of (3 − x)^n are equal in magnitude but opposite in sign. Find the value of n

answer: n=19

Thanks
 

InteGrand

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The coefficients of x^4 and x^5 in the expansion of (3 − x)^n are equal in magnitude but opposite in sign. Find the value of n

answer: n=19

Thanks
By the binomial theorem, .

The (-1)k tells us that the signs of the terms alternate, so we only need to focus on the magnitude. The above formula tells us that the coefficient of xk has magnitude .

Therefore, the absolute value of the coefficient of x4 and x5 are and .

Since we want these to be equal, we have











 

Halo189

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By the binomial theorem, .

The (-1)k tells us that the signs of the terms alternate, so we only need to focus on the magnitude. The above formula tells us that the coefficient of xk has magnitude .

Therefore, the absolute value of the coefficient of x4 and x5 are and .

Since we want these to be equal, we have











Thank you :)
 

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