JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_1=b_1=1\) and \(a_n=a_{n-1}+(n-1), b_n=b_{n-1}+a_{n-1}\), \(\forall n \geq 2\). If \(S =\sum \limits_{n=1}^{10} \frac{ b _{ n }}{2^{ n }}\) and \(T =\sum \limits_{ n =1}^8 \frac{ n }{2^{ n -1}}\), then \(2^7(2 S\) \(- T )\) is equal to \(........\).
- A \(461\)
- B \(460\)
- C \(462\)
- D \(465\)
Answer & Solution
Correct Answer
(A) \(461\)
Step-by-step Solution
Detailed explanation
\(\text { As, } S=\frac{b_1}{2}+\frac{b_2}{2^2}+\ldots \ldots .+\frac{b_9}{2^9}+\frac{b_{10}}{2^{10}}\) \(\Rightarrow \frac{S}{2}=\quad \frac{b_1}{2^2}+\frac{b_2}{2^3}+\ldots \ldots+\frac{b_9}{2^{10}}+\frac{b_{10}}{2^{11}}\) \(\text { subtracting }\)…
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