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NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

The value of ∑ i = 1 n C n + 1 i - C n i is equal to

Options

  1. A2 n
  2. B2 n + 1
  3. C3 ⋅ 2 n
  4. D2 n - 1

Correct answer

D. 2 n - 1

Step-by-step solution

C n + 1 i - C n i = C n i + C n i - 1 - C n i = C n i - 1 ⇒ Sum = C 0 n + C 1 n + … + C n - 1 n = 2 n - C n n = 2 n - 1

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