The comparison test states that if a series of positive numbers converges, and in another series, each of the corresponding terms is smaller, then it too must converge. Similarly, if a series of positive numbers diverges to infinity, and another series has each of its terms greater than the corresponding terms of the other, then it too diverges.
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When you take the integral using the series as integrand, it converges if the integral worked out to be a number. If it's infinte, the series diverge.
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In a comparison of two categories, a relationship that holds among several groups can change or even reverse when combining the groups.
IQ tests are standardized for age ranges. You divide the age of the test subject into the 'age' he tested as normal for and multiply by 100 to get IQ. For instance if you are 16 and test as having the knowledge of the average 20 year old then your IQ= (20/16)*100 = 120 Added: Not only the knowledge of the older person, or younger person, but the abilities shown on the G laden portion of the test, the part of the test monitored by a stopwatch. Such things as reverse span, counting off a series of numbers backwards, mental reaction time, know how old someone is, say, born in 1934, and rotating objects in space, pattern comparison.
a ratio is a comparison of 2 numbers