JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_{1}, a_{2}, a_{3}, \ldots\) be an \(A.P.\) If \(\sum_{r=1}^{\infty} \frac{a_{r}}{2^{r}}=4\), then \(4 a_{2}\) is equal to
- A \(15\)
- B \(16\)
- C \(14\)
- D \(13\)
Answer & Solution
Correct Answer
(B) \(16\)
Step-by-step Solution
Detailed explanation
\(S=\frac{a_{1}}{2}+\frac{a_{2}}{2^{2}}+\frac{a_{3}}{2^{3}}+\ldots\) \(\frac{S}{2} =\frac{a_{1}}{2^{2}}+\frac{a_{2}}{2^{3}}+\ldots\) \(\frac{S}{2}=\frac{a_{1}}{2}+d\left(\frac{1}{2^{2}}+\frac{1}{2^{3}}+\ldots\right)\)…
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