MAT 266 Study Guide - Midterm Guide: Binomial Coefficient, Malyshev Factory, Parametric Equation
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For most series, you cannot find the exact sum, instead using tests you should be able to determine convergence, and divergence. =() 0 is decreasing and the series =() h h. Since it goes to infinity, it diverges n. If the value of the function is greater than 1, it converges. If it is less than or equal to 1, it diverges. When you take a series and split it in two, if both functions are convergent than the parent function is convergent too. You use the ratio test for functions that contain factorials as well as exponential functions. This is because other functions when it equals 1, you cannot tell whether or not the function is convergent or divergent. =1 lim + 1 h < 1 , > 1 = 1 . Plug into standard form and put like terms together. Substitute n+1 for all the n"s in the function and then multiply by the reciprocal.
