NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The coefficient of x 6 in 1 + x 6 + 1 + x 7 + … + 1 + x 15 is

Options

AC 16 9
BC 16 5 - C 16 5
CC 16 6 - 1
DC 16 6

Correct answer

A. C 16 9

Step-by-step solution

Required coefficient is C 6 6 + C 6 7 + C 6 8 + … + C 6 14 + C 6 15 = C 7 7 + C 7 6 + C 8 6 + … + C 6 + 14 C 6 15 = C 7 8 + C 6 8 + C 6 9 + … + C 6 14 + C 6 15 = C 7 9 + C 6 9 + … + C 6 14 + C 6 15 Adding in the same order = C 7 16 = C 9 16

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