JEE Mains · Maths · STD 11 - 8. sequence and series
The value of \(1^3 - 2^3 + 3^3 - \ldots + 15^3\) is:
- A \(1706\)
- B \(1856\)
- C \(1982\)
- D \(2403\)
Answer & Solution
Correct Answer
(B) \(1856\)
Step-by-step Solution
Detailed explanation
The given series is \(S = 1^3 - 2^3 + 3^3 - 4^3 + \ldots + 15^3\). This can be rewritten as the sum of all cubes up to \(15\) minus twice the sum of cubes of even numbers up to \(14\): \(S = (1^3 + 2^3 + 3^3 + \ldots + 15^3) - 2(2^3 + 4^3 + 6^3 + \ldots + 14^3)\)…
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