What is n 2 log 2 N?
Taking big O of the second function (ignoring constants), ( log n + 1) ( n 2 + 1) we get O ( n 2 log n). We can't really ignore the exponent. Expanding the first part, we get: The n 2 log 2 n term dominates all other terms, so we conclude that it is O ( n 2 log 2 n).
Does n converge if and only if p > 1?
Thus the series ? n = 1 ? 1 / n p will converge if and only if | 2 1 ? p | < 1, which happens if and only if p > 1 (why? Try to proving it just using the laws of exponentiation, and without using logarithms).
How do you determine if an = (1 + 1 n2)n converges?
How do you determine if an = (1 + 1 n2)n converge and find the limits when they exist? lim n?? an ? lim n?? e1 n = 1 and the sequence an converges.
Should I always choose O(n log n) over n 2?
Or can we say on an average n log n out performs n 2. If I want to make one of the algorithm as default sorting algorithm of my system then should I always choose O ( n log n) over O ( n 2) . Please give some input. No. Suppose sorting algorithm A takes 1000 n log ( n) steps and algorithm B takes n 2 steps and we need to sort 1000 elements.
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Proof of p-series convergence criteria (article) | Khan Academy
If p=1, then the the p-series is divergent by definition, as a divergent p-series has a value of p greater than zero but lesser than or equal to 1 (as given in this article and the Harmonic series and p-series video in this lesson). But then, in a harmonic p-series whose p value is 1, don't the terms get smaller and smaller as the series goes on? lgo algo-sr relsrch fst richAlgo" data-47b="645f5e08d9791">www.khanacademy.org › math › ap-calculus-bcProof of p-series convergence criteria (article) | Khan Academy www.khanacademy.org › math › ap-calculus-bc Cached
Lectures 11 - 13 : Infinite Series Convergence tests