AP EAMCET · Maths · Permutation Combination
If \(n\) is a positive integer, then \(\sum_{r=1}^n r \cdot C_r=\)
- A \(2^{n-1}\)
- B \(n 2^{n-1}\)
- C \(n 2^{n+1}\)
- D \(2^{n+1}\)
Answer & Solution
Correct Answer
(B) \(n 2^{n-1}\)
Step-by-step Solution
Detailed explanation
\(\sum_{r=1}^n r \cdot C_r\) \(=1 C_1+2 C_2+3 C_3+\ldots+\ldots+n C_n=n \cdot 2^{n-1}\)
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