Unformatted text preview: 3. Geometrically, we chart the progress of the partial sums as in the figure below: 4. The series converges at the righthand endpoint. As shown in the picture above, the partial sums are closing in on some limit L as they oscillate left and right by constantly decreasing amounts. 5. We know that the series does not converge absolutely at the righthand endpoint, because ∑ } 1 n } diverges (Exploration 1 of this section). Quick Review 9.4 1. lim n → ‘ } n n 1 ) x ) 1 } 5 ) x ) lim n → ‘ } n 1 n 1 }5 ) x ) 2. lim n → ‘ } n n ( 2 n ) x 1 2 1 3 ) ) } 5 ) x 2 3 ) lim n → ‘ } n 2 n 1 2 n } 5 ) x 2 3 ) 3. lim n → ‘ } ) n x ) ! n } 5 (Note: This limit is similar to the limit which is discussed at the end of Example 3 in Section 9.3.) 4. lim n → ‘ } ( n 1 (2 n 1 ) ) 4 4 x 2 }5 x 2 lim n → ‘ 5 x 2 1 } 1 1 6 } 2 5 } 1 x 6 2 } 5. lim n → ‘ 5 lim n → ‘ } ) 2 x 2 1 1 ) } 5 } ) 2 x 2 1 1 ) } 6. Since n 2 . 5 n for n $ 6, a n 5 n 2 , b n 5 5 n , and N 5 6....
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 Spring '08
 GERMAN
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