JEE Mains · Maths · STD 11 - 8. sequence and series
If \(1+\left(1-2^{2} \cdot 1\right)+\left(1-4^{2} \cdot 3\right)+\left(1-6^{2} \cdot 5\right)+\ldots \ldots+\left(1-20^{2} \cdot 19\right)\) \(=\alpha-220 \beta,\) then an ordered pair \((\alpha, \beta)\) is equal to
- A \((10,97)\)
- B \((11,103)\)
- C \((10,103)\)
- D \((11,97)\)
Answer & Solution
Correct Answer
(B) \((11,103)\)
Step-by-step Solution
Detailed explanation
\(1+\left(1-2^{2} \cdot 1\right)+\left(1-4^{2} \cdot 3\right)+\ldots \ldots+\left(1-20^{2} \cdot 19\right)\) \(=\alpha-220 \beta\) \(=11-\left(2^{2} \cdot 1+4^{2} \cdot 3+\ldots \ldots+20^{2} \cdot 19\right)\)…
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