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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2015 · Mathematics · Binomial Theorem

What is (∑_ r=0 ^1 n+r n ) equal to?

What is (\sum_{r=0}^1\binom{n+r}{n}) equal to?

Options

  1. A(\binom{n+2}{1})
  2. B(\binom{n+3}{n})
  3. C(\binom{n+2}{n})
  4. D(\binom{n+2}{n+1})

Correct answer

A. (\binom{n+2}{1})

Step-by-step solution

(\sum_{r=0}^1\binom{n+r}{n}=\binom{n}{n}+\binom{n+1}{n}=1+(n+1)=n+2=\binom{n+2}{1})
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