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the least postitive interger n from which `root(3) (n+1) -root(3)(n)lt (1)/(12)` is -A. 6B. 7C. 8D. 9 |
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Answer» Correct Answer - C `(n+1)^(1//3)-n^(1//3) lt (1)/(12) ` ` (n+1)-n-3(n+1)^(1//3)n^(1//3)-n^(1//3)lt ((1)/(12))^(3)` ` 1-3n^(1//3) (n+1)^(1//3)xx(1)/(12)lt (1)/((12)^(3))` `(12)^(3) -3.(12)^(2) n^(1//3)(n+1)^(1//3) lt 1` ` (12)^(3) -1lt 3.(12)^(12)n^(1//3)(n+1)^(1//3)` `(1727)/(3xx144)lt n^(1//3)(n+1)^(1//3)` `n(n+1)gt((1727)/(3xx144))^(3)` `n(n+1)gt 63.88` `n=8` |
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