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Question: Answered & Verified by Expert
If \(n\) is a positive integer, then \(\sum_{r=1}^n r \cdot C_r=\)
MathematicsPermutation CombinationAP EAMCETAP EAMCET 2020 (17 Sep Shift 2)
Options:
  • A \(2^{n-1}\)
  • B \(n 2^{n-1}\)
  • C \(n 2^{n+1}\)
  • D \(2^{n+1}\)
Solution:
2995 Upvotes Verified Answer
The correct answer is: \(n 2^{n-1}\)
\(\sum_{r=1}^n r \cdot C_r\)
\(=1 C_1+2 C_2+3 C_3+\ldots+\ldots+n C_n=n \cdot 2^{n-1}\)

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