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Unformatted text preview: n lim
n ( 2 n 1) 31 / n
n ( 2 n 1) 3 Since we have infinity / infinity, we can do l’hopitals rule, but you can see that doing this three times will leave the denominator as a constant, and the numerator as en. This means we get: lim an
n 1/ n en lim n c Thus the series diverges by the root test. Summary of Strategies Thus Far
Geometric Series Test When we have something that looks like arn
Divergent Series Test Should always quickly check first to see if the limit goes to a number
Telescoping Series Happens when we can separate the series into a difference of two series
Integral Test When the function can be integrated
Comparison/Limit Comparison Test Polynomials/Polynomials (or last resort for some tougher series)
Alternating Series Test Need I say more?
Ratio Test When we have factorials and/or exponentials
Root Test When we have f(n)g(n) and other exponentials...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.
- Summer '00
- Calculus, Lecture Notes, MATH1004, Kyle Harvey