WBJEE · Maths · Sequences and Series
Let \(S\) denote the sum of the infinite series \(1+\frac{8}{2 !}+\frac{21}{3 !}+\frac{40}{4 !}+\frac{65}{5 !}+\ldots .\) Then
- A \(S < 8\)
- B \(S>12\)
- C \(8 < S < 12\)
- D \(S=8\)
Answer & Solution
Correct Answer
(C) \(8 < S < 12\)
Step-by-step Solution
Detailed explanation
Let \(S=1+\frac{8}{2 !}+\frac{21}{3 !}+\frac{40}{4 !}+\frac{65}{5 !}+\ldots\) Again, let \(S_{1}=1+8+21+40+65+\ldots+T_{n}\) and \(\quad S_{1}=+1+8+21+40+\ldots+T_{n}\)…
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