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Probability Level 2

What is the coefficient of x 98 x^{98} in the expansion of ( x + 2 ) 100 (x+2)^{100} ?


The answer is 19800.

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Rafel Permata Syukur Ramadhan by Rafel Permata Syukur Ram… , 23

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3 solutions

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Caleb Townsend
Mar 3, 2015

In general, the coefficient of x n − 2 x^{n - 2} in ( x + 2 ) n (x + 2)^n is 2 n ( n − 1 ) . 2n(n-1). This formula can be proven by induction. Substitute n = 100 n = 100 and you get 200 × 99 = 19800 200\times99 =\boxed{19800}

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Irtaza Sheikh
Apr 30, 2015

Formula is applied Tr+1=(nCr)×a^n-r × b^r
Just put a= x and b=2
As we know that z^98 is possible if r= 2
Then 100C2=4950 ×4= 19800 ans


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