If \(n\) is a positive integer, then \(\sum_{r=1}^n r \cdot C_r=\)

If \(n\) is a positive integer, then \(\sum_{r=1}^n r \cdot C_r=\)
  1. \(2^{n-1}\)
  2. \(n 2^{n-1}\)
  3. \(n 2^{n+1}\)
  4. \(2^{n+1}\)

Solution

\(\sum_{r=1}^n r \cdot C_r\) \(=1 C_1+2 C_2+3 C_3+\ldots+\ldots+n C_n=n \cdot 2^{n-1}\)

Asked in: AP EAMCET 2020 (17 Sep Shift 2)

Practice more Permutation Combination questions on Aicharya