COMEDK · Maths · 5. Sequences and Series
\(\frac{1}{3 !}+\frac{2}{5 !}+\frac{3}{7 !}+\ldots\) to \(\infty\) is equal to
- A \(e\)
- B \(2 e\)
- C \(\frac{1}{2 e}\)
- D \(\frac{e}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2 e}\)
Step-by-step Solution
Detailed explanation
\(n\)th term \(=\frac{n}{(2 n+1) !}\) \(=\frac{1}{2}\left[\frac{(2 n+1)-1}{(2 n+1) !}\right]=\frac{1}{2}\left[\frac{1}{(2 n) !}-\frac{1}{(2 n+1) !}\right]\) \(\therefore\) Sum of the series…
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