InterviewSolution
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InterviewSolution
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Which of the following sequences are unbounded?A. `(1+(1)/(n))^(n)`B. `((2n+1)/(n+2))`C. `(1+(1)/(n))^(n^(2))`D. `tan n` |
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Answer» Correct Answer - C::D (c ) `:.a_(n) =(1+(1)/(n))^(n^(2))` For `n=1,a_(1)=2`, for `n=2,a_(2)=(1+(1)/(2))^(4)=((3)/(2))^(4)=(3^(4))/(2^(4))=(81)/(16)=5.06" " [" approximate "]` `lim_(nto oo)(1+(1)/(n))^(n^(2))=e^(lim_(nto oo)(1)/(n)xx^(n^(2)))=e^(lim_(nto oo)n)=e^(oo)=oo` `:.{a_(n)}` represents unbounded sequence. (b) `:.a_(n)=tann` `a_(n)=n+(n^(3))/(3)+(2)/(15)n^(5)+"...."+oo` and we know that `-oolttan nltoo` So, `{a_(n)}` is unbounded sequence. |
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