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Statement-1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ... + (361 + 380 + 400) is 8000. Statement-2: ∑(k=1 to n) (k^3 - (k - 1)^3) = n^3, for any natural number n.

1. Statement-1 is false, Statement-2 is true.
2. Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.
3. Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.
4. Statement-1 is true, statement-2 is false.

Correct answer: Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.

Solution

Statement-1 accurately represents the sum of the series, which totals 8000, while Statement-2 correctly demonstrates a mathematical identity that supports the structure of the series in Statement-1, making it a valid explanation.

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