Consider the sequences a n </msub> and b n </msub> , where a

Isaiah Farrell

Isaiah Farrell

Answered question

2022-05-21

Consider the sequences a n and b n , where
a n = n ( 2 n + 1 ) n 2 and b n = ( 1 ) n 5

Which of the sequences converge and which diverge? If it converges, indicate its limit

Answer & Explanation

aniizl

aniizl

Beginner2022-05-22Added 12 answers

Consider:
a n = n ( 2 n + 1 ) n 2 and b n = ( 1 ) n 5

Now, lim n a n = lim n n ( 2 n + 1 ) n 2
= lim n 2 n 2 + n n 2
= lim n ( 2 + 1 n )
= 2 + 0 = 2
Thus, a n converges and its limit is 2

Given b n = ( 1 ) n 5
b n = { 1 5   i f   n   i s   e v e n   1 5   i f   n   i s   o d d

This sequence is divergent as it has two limits 1 5 , 1 5

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