Q78 / 160 · AP EAMCET 2020 (17 Sep Shift 2) · Mathematics

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

  • A
    \(2^{n-1}\)
  • Correct answer
    B
    \(n 2^{n-1}\)
  • C
    \(n 2^{n+1}\)
  • D
    \(2^{n+1}\)

Solution

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

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

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