Statement-1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) +.....+ (361 + 380 + 400) is 8000. Statement-2: Σ k = 1 ⁿ (k³ - (k - 1)³) = n³, for any natural number n.

(B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

(A) Statement-1 is false, Statement-2 is true.

(C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(D) Statement-1 is true, Statement-2 is false.

Sequence and Series: JEE Main 2012 Mathematics question

JEE Main 2012 · Annual, Paper 1 · Q5289

JEE Main 2012Annual, Paper 1MathematicsMediumSequence and Series179× since 2002

Statement-1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) +.....+ (361 + 380 + 400) is 8000. Statement-2:

\sum\limits_{k = 1}^n {\left( {{k^3} - {{(k - 1)}^3}} \right)} = {n^3}

, for any natural number n.

JEE Main 2012 · Annual, Paper 1 · Q5289

JEE Main 2012Annual, Paper 1MathematicsMediumSequence and Series179× since 2002

Statement-1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) +.....+ (361 + 380 + 400) is 8000. Statement-2:

\sum\limits_{k = 1}^n {\left( {{k^3} - {{(k - 1)}^3}} \right)} = {n^3}

, for any natural number n.