WBJEE · Maths · Binomial Theorem
The value of \(\sum_{r=2}^{\infty} \frac{1+2+\quad+(r-1)}{r !}\)
- A \(e\)
- B \(2 e\)
- C \(\frac{e}{2}\)
- D \(\frac{3 e}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{e}{2}\)
Step-by-step Solution
Detailed explanation
\(\sum_{r=2}^{\infty} \frac{(r-1) r}{2 r !}=\sum_{r=2}^{\infty} \frac{1}{2(r-2) !}\) \(=\frac{1}{2}\left[\frac{1}{0 !}+\frac{1}{1 !}+\frac{1}{2 !}+\quad \infty\right]=\frac{1}{2} e\)
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