JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(\left\{a_{n}\right\}_{n-1}^{\infty}\) be a sequence such that \(a_{1}=1, a_{2}=1\) and \(a_{n+2}=2 a_{n+1}+a_{n}\) for all \(n \geq 1 .\) Then tha value of \(47 \sum_{n=1}^{\infty} \frac{a_{n}}{2^{3 n}}\) is equal to \(.....\)
- A \(4\)
- B \(7\)
- C \(11\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(7\)
Step-by-step Solution
Detailed explanation
\(a_{n+2}=2 a_{n+1}+a_{n}, \text { let } \sum_{n=1}^{\infty} \frac{a_{n}}{8^{n}}=P\) Divide by \(8^{\mathrm{n}}\) we get \(\frac{a_{n+2}}{8^{n}}=\frac{2 a_{n+1}}{8^{n}}+\frac{a_{n}}{8^{n}}\)…
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