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99 Percentile Qs Bank for JEE MainMathematicsLimits

lim n → ∞ ⁡ 1 2 1 - n 3 + 2 2 1 - n 3 + . . . + n 2 1 - n 3 is equal to

Options

A1 3
B- 1 6
C1 6
D- 1 3

Correct answer

D. - 1 3

Step-by-step solution

lim n → ∞ 1 1 - n 3 ⁡ ∑ r = 1 n r 2 = lim n → ∞ 1 n 3 1 n 3 - 1 n n + 1 ( 2 n + 1 ) 6 = l i m n → ∞ n 3 1 + 1 n 2 + 1 n n 3 1 n 3 - 1 6 = - 1 3

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