Directions find the sum of the series 95 n 1 tan3 n

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Precalculus: A Concise Course
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Chapter 1 / Exercise 67
Precalculus: A Concise Course
Larson
Expert Verified
Directions: Find the sum of the series. 95. n =1 tan(3 n ) 96. n =2 4 n ( n + 2) 97. n =1 4(0 . 3) n - 1 Directions: Determine (a) whether { a n } is convergent, and (b) whether n =1 a n is convergent. 98. a n = 7 n 2 n + 1 Directions: Determine whether the series converges or diverges. If it is convergent, find the sum. Determine (a) the values of x for which the series converges, and (b) the sum of the series for those values. 107. n =1 x n 4 n Directions: Answer the questions. 108. If a n and b n are both divergent, is ( a n + b n ) necessarily divergent? 109. Consider the series n =1 n ( n + 1)! . (a) Find the partial sums s 1 , s 2 , s 3 , and s 4 . Do you recognize the denominators? (b) Use the pattern to get a formula for s n . (c) Show that the given infinite series is convergent, and find its sum. 99. 8 n 100. n =1 n 20 101. n =1 ln n 2 + 1 8 n 2 + 5 102. k =1 cos k 1 103. n =1 3 e n + 2 n ( n + 1) 104. n =1 e n n 7 105. n =2 2 n 2 - 1 106. n =1 ( e 1 /n - e 1 / ( n +1) ) Determine whether the series converges or diverges. 110. n =1 ne - 6 n 111. n =1 3 ln n n 5 112. n =1 e 1 /n 9 n 10 113. n =1 n 2 e 9 n 114. n =1 n 9 n 20 + 1 Directions: Find the values of p for which the series is convergent. 115. n =2 5 n (ln n ) p n =1 1 + 5 n Directions: Determine (a) the values of x for which the series converges, and (b) the sum of the series for those values. 107. n =1 x n 4 n Directions: Answer the questions. 108. If a n and b n are both divergent, is ( a n + b n ) necessarily divergent? 109. Consider the series n =1 n ( n + 1)! . (a) Find the partial sums s 1 , s 2 , s 3 , and s 4 . Do you recognize the denominators? (b) Use the pattern to get a formula for s n . (c) Show that the given infinite series is convergent, and find its sum. Integral Test Directions: Determine whether the series converges or diverges. 110. n =1 ne - 6 n 111. n =1 3 ln n n 5 112. n =1 e 1 /n 9 n 10 113. n =1 n 2 e 9 n 114. n =1 n 9 n 20 + 1 Directions: Find the values of p for which the series is convergent. 115. n =2 5 n (ln n ) p
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Precalculus: A Concise Course
The document you are viewing contains questions related to this textbook.
Chapter 1 / Exercise 67
Precalculus: A Concise Course
Larson
Expert Verified
Comparison Tests Directions: Determine whether the series converges or diverges. 116. n =1 n 2 + 1 n 2 n 117. n =1 6 n 4 + 11 n 118. n =1 sin 2 n n 2 + 4 119. n =0 3 + cos n 7 n 120. n =5 6 n n - 4 121. n =1 n + 5 n n + 8 n 122. n =1 2 + n + 2 n 2 1 + n 2 + n 6 123. n =1 1 + 1 n 2 e - 4 n 124. n =1 5 sin(3 /n ) Alternating Series Test Directions: Determine whether the series converges or diverges. 125. n =1 ( - 1) n - 1 ln(4 n + 5) 126. n =1 ( - 1) n n 1 + 3 n 127. n =3 ( - 1) n - 1 4 e 1 /n n 128. n =2 ( - 1) n 10 n ln n 129. n =1 ( - 1) n - 1 ln n n 130. n =1 cos n π n 3 / 5 131. n =1 ( - 1) n sin( π /n ) Directions: Show that the series is convergent. According to the Alternating Series Sum Estimation Theorem, how many terms of the series do we need to add in order to find the sum to the indicated accuracy? 132. n =1 ( - 1) n +1 n 7 ( | error | < 0 . 00005) 133. n =1 ( - 1) n n 5 n ( | error | < 0 . 0001) 134. n =0 ( - 1) n 8 n n ! ( | error | < 0 . 000005) Directions: Approximate the sum of the series correct to four decimal places. 135. n =0 ( - 1) n - 1 n 2 8 n Ratio and Root Tests Directions: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 136. n =0 ( - 11) n n ! 137. n =1 ( - 1) n - 1 3 n n 4 138. n =1 ( - 1) n n n 3 + 5
139. n =1 ( - 1) n e 1 /n n 7 140. n =1 sin 4 n 7 n 141. n =1 12 n ( n + 1)8 2 n +1 142. n =1 ( - 1) n +1 n 8 5 n n ! 143. n =1 ( - 1) n arctan n n 12

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