JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(A\) be the sum of the first \(20\) terms and \(B\) be the sum of the first \(40\) terms of the series \({1^2} + 2 \cdot {2^2} + {3^2} + 2 \cdot {4^2} + {5^2} + .\;.\;.\;.\).If \(B - 2A = 100\lambda \) then \(\lambda \) is equal to :
- A \(248\)
- B \(464\)
- C \(496\)
- D \(232\)
Answer & Solution
Correct Answer
(A) \(248\)
Step-by-step Solution
Detailed explanation
(1) Here, \(B - 2A = \) \(\sum\limits_{n = 1}^{40} {{a_n} - 2\sum\limits_{n = 1}^{20} {{a_n}} } = \sum\limits_{n = 21}^{40} {{a_n} - 2\sum\limits_{n = 1}^{20} {{a_n}} } \)…
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