$\sum_{k=1}^n k(k+1)(k+2) \ldots(k+r-1)=$

• Correct answer
  A

  $\frac{n(n+1)(n+2) \ldots(n+r)}{r+1}$
• B

  $\frac{n(n+1)(n+2) \ldots(n+r-1)}{r}$
• C

  $\frac{\mathrm{n}(\mathrm{n}+1)(\mathrm{n}+2) \ldots(\mathrm{n}+\mathrm{r}+1)}{\mathrm{r}+1}$
• D

  $\frac{n(n+1)(n+2) \ldots 2 n}{2 n+1}$

Hence, the correct answer is option: 'A'.