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Infinite Sequences

Question #3 (Medium): Convergent Sequence and Finding Its Limit

Strategy

The long and tedious way would be to plug in each n number for the terms in the sequence and observe

if the pattern is convergent or divergent. This may not always be correct. Much better approach is to

determine the convergence and divergence systematically by treating the n as a variable, simplifying and

applying limit to it as

Sample Question

Determine if the sequence converges or diverges. If it converges, find the limit.

Solution

Treating the n as a variable, the general sequence formula can be simplified. Plugging in is of no

use at this point as both numerator and denominator will approach .

Divide top and bottom by then:

As :

Therefore the sequence converges to the value of .

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