MTH 253 – Calculus (Other Topics)Chapter 10 Review1. Given the first few terms of a sequence, determine a formula for the general term.2. Given a sequence, find its limit or determine that it is divergent.3. Determine whether a sequence is monotone or strictly monotone or neither.a. Consider differences of successive terms.b. Consider ratios of successive termsc. Consider the derivative of the associated continuous function.4. Determine if a monotone sequence is convergent or divergent.5. Find several partial sums of a series and use the nth partial sum to determine if a series converges or diverges.6. Evaluate the sum of a geometric series. 0 if 11diverges otherwisekkararr�=�<�=-����7. Tests For Convergence: Series w/ all terms non-negative (name, state, & use these)a. Divergence Testb. Integral Testc. p-Seriesd. Comparison Teste. Limit Comparison Testf. Ratio Testg. Root Test8. Tests For Convergence: Series w/ negative & positive terms (name, state, & use these)a. Geometric Seriesb. Alternating Series Testc. Absolute Convergence Test9. Types of Convergencea. Converge Absolutelyb. Diverge Absolutelyc. Converge Conditionally10. Maclaurin ( )00x = & Taylor Polynomials( )000( )( ) ( )!knknkf xp x x xk== -�11. Error Estimation:a. Alternating Series: Error � first term not used.b. nth Remainder Estimation (formula will be given)01( 1)0[ , ]Error ( ) where ( )( 1)!nnnx xMR x x x M f xn++� � - �+12. Maclaurin ( )00x = & Taylor Series and their Intervals of Convergence( )00 0 0 00?( )( ) ( ) ( , ) !kknkf xp x x x x x R x R x x Rk�== - � - + = ��13. Operations on Power Series to Obtain the Power Series for Other Functionsa. Substitution (i.e. let ( )x f x=)b. Differentiatec. Integrated. Add/Subtracte.
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