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Question:

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)^n (k³ - ((k - 1)³) = n³, for any natural number n.

Statement 1 is false, Statement 2 is true.

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

Statement 1 is true , Statement 2 is false.

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

Solution:

Tk = (k - 1)² + k(k - 1) + k² = (k³ - (k - 1)³)/(k - 1) - k = k³ - (k - 1)³