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# How to find the limit sequence?

Last updated date: 13th Jul 2024
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If the sequence is such that, the higher terms are smaller in magnitude and the difference of the consecutive terms is decreased as the order of the terms is increased then the limit point is obtained. The example for it is ${\left\{ {\dfrac{1}{n}} \right\}_n} = \left\{ {1,\dfrac{1}{2},\dfrac{1}{3},...} \right\}$ in this case the limit is zero as the higher the terms are the closer the value get is 0 and for large value of n the expression is infinity. Then $\mathop {\lim }\limits_{n \to \infty } \dfrac{1}{n} = 0$ this is known as the limit point. The two things to be answered, the limit point is unique for every sequence, the second limit point may not be the member of the sequence as it is in this that is zero.
${\left\{ {\left\{ {{{\left( { - 1} \right)}^n}} \right\}} \right\}_n} = \left\{ { - 1,1, - 1,1,...} \right\}$
As we know that there are some other type of sequence in which the consecutive term is increased in the magnitude for the higher value of n and the difference between the two terms is increased and the sequence that diverges altogether, then, ${\left\{ n \right\}_n} = \left\{ {1,2,3} \right\}$, here the limit n tends to infinity.