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JEE Main202311 Apr 2023Morning ShiftMathematicsBinomial TheoremActual

The mean of the coefficients of x , x 2 , … … , x 7 in the binomial expression of ( 2 + x ) 9 is _________

Correct answer

0

Step-by-step solution

We know that. Binomial expansion of 2 + x 9 is given by, 2 + x 9 = C 0 9 x 0 2 9 + C 1 9 x 1 2 8 + . . . . . . . . . . . C 9 9 x 9 2 0 Now put x = 1 we get, 2 + 1 9 = C 0 9 2 9 + C 1 9 2 8 + + C 2 9 2 7 + . . . . . . . . . . . C 9 9 2 0 ⇒ 3 9 = C 0 9 2 9 + C 1 9 2 8 + + C 2 9 2 7 + . . . . . . . . . . . C 9 9 2 0 So, sum of coefficient of x ,   x 2 ,   x 3 ,   . . . . . . . . . ,   x 7 will be, ⇒ C 1 9 2 8 + C 2 9 2 7 + . . . . . . . . . . . C 7 9 2 2 = 3 9 - C 0 9 2 9 - C 8 9 2 1 -

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