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What sequence has no upper bound but does not tend to infinity?
If I understand your question correctly, such a sequence is an = x cos(πx). It has neither an upper nor lower bound. It's divergent, but its limit is neither infinity nor negative infinity.
What does limit mean in writing?
Students surely can recognize the number that is the limit of this sequence.
What is limit as x approaches 0 of cos squared x by x?
The limit of cos2(x)/x as x approaches 0 does not exist. As x approaches 0 from the left, the limit is negative infinity. As x approaches 0 from the right, the limit is positive infinity. These two values would have to be equal for a limit to exist.
What is the limit of the ratio of consecutive terms of the Fibonacci sequence?
The limit of the ratio is the Golden ratio, or [1 + sqrt(5)]/2
What is convergence in numeric math?
A sequence of numbers, xn (where n = 1, 2, 3, ...), is said to converge to a limit L if, given any positive e, however small, it is possible to find an integer k such that |xn - L| < e for all n > k.In other words, after a certain point (k) all terms of the sequence are closer to the limit (L) than any tiny number.
