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Kummer
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Prove that [tex]\sin (n^2) + \sin (n^3)[/tex] is not a convergent sequence.
I believe that is easier. Consider n=3,31,314,3141,31415,...mathwonk said:how about just sin(n).
In mathematics, convergence refers to the idea that a sequence or series of numbers approaches a specific value as the number of terms increases.
A convergent sequence approaches a specific value as the number of terms increases, while a divergent sequence does not have a specific limit and can either approach infinity or oscillate between values.
To prove that a sequence is not convergent, we need to show that it either approaches infinity or oscillates between values. In this case, we can show that the sequence sin(n^2) + sin(n^3) does not approach a specific value as the number of terms increases, therefore it is not convergent.
The limit of this sequence does not exist, as the values oscillate between -2 and 2 as n increases. Therefore, the sequence is not convergent.
Proving that a sequence is not convergent is important in understanding the behavior of the sequence and its limit. It also helps in identifying patterns and relationships between different sequences, which can be useful in solving complex mathematical problems.