JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(n \in N\) and \([x]\) denote the greatest integer less than or equal to \(x\). If the sum of \((n+1)\) terms \({ }^{n} C_{0}, 3 .{ }^{n} C_{1}, 5 .{ }^{n} C_{2}, 7 .{ }^{n} C_{3}, \ldots\) is equal to \(2^{100} \cdot 101\), then \(2\left[\frac{n-1}{2}\right]\) is equal to \(....\)
- A \(40\)
- B \(11\)
- C \(45\)
- D \(98\)
Answer & Solution
Correct Answer
(D) \(98\)
Step-by-step Solution
Detailed explanation
\(1 .^{n} C_{0}+3 \cdot{ }^{n} C_{1}+5 .^{n} C_{2}+\ldots+(2 n+1) \cdot \cdot ^{n}C_{n}\) \(\mathrm{T}_{\mathrm{r}}=(2 \mathrm{r}+1)^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}\) \(\mathrm{S}=\Sigma \mathrm{T}_{\mathrm{r}}\)…
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