JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Application +4 | -1

Let

z_n=\frac{1^3+2^3+3^3+\cdots+n^3}{n^4}

Then

\lim _{n \rightarrow \infty} z_n

View answer and explanation

Correct option: C

\frac{1}{4}

Option C (

\frac{1}{4}

) is correct because the sum of the cubes of the first n natural numbers is

\frac{n^2(n+1)^2}{4}

, and dividing by

n^4

and taking the limit as

n

approaches infinity yields

\frac{1}{4}

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