Exercises.pdf

# Exercises.pdf - Sequences and Series Exercises Sampoerna...

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Sequences and Series Exercises Sampoerna Academy Boarding School (1) Write the first five terms of the sequence, determine the convergence or divergence or the sequence. If the sequence converges, find its limit. a n = 2 3 n + 1 a n = n 2 + 2 n a n = n n 2 + 1 a n = 3 - 2 n a n = n ln n a n = sin n n (2) Write an expression for the n -th term of the given sequence. 2 , 8 , 14 , 20 , 26 , . . . • - 7 , - 3 , 1 , 5 , 9 , . . . 1 , 1 2 , 1 6 , 1 24 , 1 120 , . . . • - 2 , 4 , - 8 , 16 , - 32 , 64 , . . . 7 , - 7 , 7 , - 7 , 7 , - 7 , . . . (3) The following sequences defined recursively, write the first five terms of the sequnce. Also, determine whether it is convergent or divergent. a 1 = 2 , a n +1 = 3 a n a 1 = - 1 , a n +1 = 0 . 5 a n a 1 = 1 , a n +1 = 2 a n + 5 (4) Find the sum of the convergent series. n =0 3 5 n n =0 2 n - 1 3 n +1 n =0 2 n + 3 n +1 5 n n =0 1 n 2 + 3 n + 2 7 , - 7 , 7 , - 7 , 7 , - 7 , . . . (5) Use n -th term test to determine whether the given series is divergent (or by any other method).

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• Fall '11
• Staff
• Mathematical Series, Sampoerna Academy Boarding School, ​ n, Use n-th term test

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