Evaluate \( \lim _{n \rightarrow \infty} \frac{[x]+[4 x]+[7 x]+\ldots+[(3 n-2) x]}{n^{2}} \) whe...
Evaluate \( \lim _{n \rightarrow \infty} \frac{[x]+[4 x]+[7 x]+\ldots+[(3 n-2) x]}{n^{2}} \) where \( [ \). denotes greatest integer function.
(a) \( \frac{2}{3} x \)
(b) \( \frac{3}{2} x \)
(c) \( \frac{1}{2} x \)
(d) \( \frac{1}{3} x \)
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