InterviewSolution
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InterviewSolution
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The value of `lim_(ntooo) [root(3)((n+1)^(2))-root(3)((n-1)^(2))]` is __________.A. Equals `(1)/(sqrt(2))`B. Does not existC. Equals `sqrt(2)`D. Equals -sqrt(2)` |
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Answer» Correct Answer - `(0)` `underset(ntooo)lim[root(3)((n+1)^(2))-root(3)((n-1)^(2))]` `=underset(ntooo)limn^(2//3)[(1+(1)/(n))^(2//3)-(1-(1)/(n))^(2//3)]` `=underset(ntooo)limn^(2//3)[(1+(2)/(3).(1)/(n)+((2)/(3)((2)/(3)-1))/(2!)(1)/(n^(2))...)-(1-(2)/(3).(1)/(n)+((2)/(3)((2)/(3)-1))/(2!)(1)/(n^(2))...)]` `=underset(ntooo)limn^(2//3)[(4)/(3).(1)/(n)+(8)/(81).(1)/(n^(3))+...]` `=underset(ntooo)lim[(4)/(3).(1)/(n^(1//3))+(8)/(81).(1)/(n^(7//3))+...]=0` |
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