This: ((1/n)*(log2n)2 + 1/√n) can be replaced with just 1/√n, because the rest is much smaller for large n, while ( √nlog3(log2n) + √nlog2n ) becomes √nlog2n for the same reason, so in the end you have 1/√n * √nlog2n, which is just log2n.
Is the above Big O notation equivalent to each other? I expanded the left side out (not shown here) and it seems that [(log n)3/√n] is the highest power.
If they are equivalent to each other, is there a simpler way of finding out why? Because I think expanding the left side out is too much work.
This: ((1/n)*(log2n)2 + 1/√n) can be replaced with just 1/√n, because the rest is much smaller for large n, while ( √nlog3(log2n) + √nlog2n ) becomes √nlog2n for the same reason, so in the end you have 1/√n * √nlog2n, which is just log2n.
So for each of the two expressions on the left, you find the highest power of each expression and then finally find the higher expression among the two remaining powers 1/√n * √nlog2n, ?
@hcoder75: General rules are dangerous in this; limits can be complicated.
@hcoder75 no, I find the largest of the expressions in left sum, ignore the rest, then the largest of the expressions in the right sum, then multiply the results. you can only ignore expressions when they are added to each other, essentially removing all unimportant ones. however, you have to multiply everything -- you cannot ignore the factors.