If s_ n = _ r=n ^ n 1 ^ n C_ r and t_ n = _ r=n ^ n r ^ n C_ r then t_ n 5 _ n is equal to

Mathematics · JEE Main · NTA ExamsBinomial Theorem And Its Simple Applications

If \(s_{n}=\sum_{r=n}^{n} \frac{1}{{ }^{n} C_{r}} \text { and } t_{n}=\sum_{r=n}^{n} \frac{r}{{ }^{n} C_{r}}\)  then \(\frac{t_{n}}{\mathbf{5}_{n}}\) is equal to
  1. \(\frac{1}{2} n\)
  2. \(\frac{1}{2} n-1\)
  3. \(\text { n - } 1\)
  4. \(\frac{2 n-1}{2}\)

Answer

(B) 1 2 n-1

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