2 101 state whether the sequence converges or

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Applied Calculus for the Managerial, Life, and Social Sciences
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Chapter 3 / Exercise 5
Applied Calculus for the Managerial, Life, and Social Sciences
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2. (10.1) State whether the sequence converges or diverges? If the sequence converges, find its limit. 1 2 2 4 2 3 2 2 2 n n n n Solution: It converges. 2 1 2 3 2 0 0 2 0 0 3 lim 2 / 1 / 2 2 ) / 4 ( ) / 2 ( 3 lim 2 / ) 1 2 2 ( / ) 4 2 3 ( lim 2 1 2 2 4 2 3 lim 2 1 2 2 4 2 3 2 lim 2 2 2 2 2 2 2 2 2 2 n n n n n n n n n n n n n n n n n n n n n n n 3 .(10.2) Does the series definitely diverge by the n th Term Test? If not, what can we conclude? 1 2 3 4 2 4 3 2 4 2 5 3 8 n n n n n n n n Solution: 0 2 4 8 ) / 3 ( ) / 1 ( ) / 1 ( ) / 2 ( 4 ) / 2 ( ) / 5 ( ) / 3 ( 8 lim / ) 3 2 4 ( / ) 2 5 3 8 ( lim 3 2 4 2 5 3 8 lim lim 4 3 2 4 3 2 4 2 3 4 4 2 4 2 3 4 2 4 n n n n n n n n n n n n n n n n n n n n n n n a n n n n n 1 2 3 4 2 4 3 2 4 2 5 3 8 n n n n n n n n diverges by the n th Term Test for Divergence. Note: The n th Term Test can only identify divergence. No convergence can be determined by this divergence test.
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Applied Calculus for the Managerial, Life, and Social Sciences
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Chapter 3 / Exercise 5
Applied Calculus for the Managerial, Life, and Social Sciences
Tan
Expert Verified
4 . (10.3) Rewrite the geometric series using the sigma notation and calculate the value of the sum. 625 81 125 27 25 9 5 3 1
5 . (10.3/Example 4) Find all values of x for which the geometric series converges and find its sum. 0 3 2 k k x
6. (10.3/Example 5/Exercise 35) Calculate the value of the partial sum for S 4 and S 5 , find a formula for general partial sum S n , and then find the limit of s n as n approaches infinity. 3 1 1 2 1 n k k ?

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