Workshop summation of series

# Workshop summation of series - a The Liebniz test should be...

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a) The Liebniz test should be used to determine the convergence of this alternating series. To use the Liebniz test, the absolute value of the alternating series should be considered, and the limit as n approaches infinity should be evaluated. As n gets larger, the nth term approaches 0. This can be seen as the denominator approaches infinity, while the numerator approaches 1. Therefore, the Liebniz test leads to the conclusion that the series converges, because the alternating series is decreasing and approaching 0. Again, the convergence of the alternating series should be determined using the Liebniz test. As stated before, the absolute value of the alternating series should be taken to use the Liebniz test. Using the Liebniz test requires that the limit as the a n term of the alternating series approaches infinity = 0. Because the sin function oscillates between -1 and 1, and because the denominator approaches infinity as n approaches infinity, the limit is equal to 0. Thus it is seen that this series is convergent because the alternating series decreases and approaches 0.

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