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NTA Abhyas JEE Main2020MathematicsBinomial TheoremPractice

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

Options

  1. A- 1 n + 1
  2. B- 1 n
  3. C1 n + 1
  4. Dn n + 1

Correct answer

D. n n + 1

Step-by-step solution

∑ r = 1 n - 1 r + 1 C r n r + 1 Using C n + 1 r + 1 = n + 1 r + 1 C n r , we get, ∑ r = 1 n - 1 r + 1 1 n + 1 C r + 1 n + 1 = 1 n + 1 ∑ r = 1 n - 1 r + 1 C r + 1 n + 1 = 1 n + 1 0 - C n + 1 0 - C n + 1 1 = 1 n + 1 0 - 1 + n + 1 = n n + 1

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