Question
Prove that the sequence is convergent where (
n) is a bounded sequence.
Answer :
Word Count : 205
To prove that the sequence \( \left\{ \frac{a_n}{n} \right\} \) is convergent where \( \{a_n\} \) is a bounded sequence, we will proceed step by step: ### Step 1: Define a bounded sequence Since ______ _________ ___ _________ _______ _______ ____ ____.
______ ____ __________ ______ _____ ____ ______ ___ ___ ______.
___ _________ ______ ___ _________.
_____ __________ ____ ________ ___ _____ ________ ________ ______.
____ ________ ___ _____ _____ ______ ______ _____ ______.
_________ ______ _________ ________ ____ __________.
____ ___ __________ _____ ___ __________ ______ ________ _________ ________ ___ ______.
__________ __________ _________ ___ ______ ________ __________ __________ ___ ___ ______ ___.
______ ________ _______ _______ ____ _____ ____ ________ __________ ________ _______.
____ _____ _________ ________ ________ ______ _______.
__________ ___ __________ _____ _____ __________ ___ ___ _______ ___.
_________ _____ __________ ______ _____ ______ _________ ________.
__________ _____ ___ __________ ______ _____ __________ __________ __________.
_______ __________ _____ _________ ______ ________ _________ _______.
______ _______ _________ _________ ______ ______ ________ ________ ____.
________ ________ _______ __________ ____ ____ _________.
_____ ______ _________ ______ _________ ______ ________.
___ _______ ____ ____ _________ ____ ______ ______.
_________ ____ __________ __________ _____ ______ __________.
_______ ________ __________ ________ ______ ______ ______ _____ ______.
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To prove that the sequence \( \left\{ \frac{a_n}{n} \right\} \) is convergent where \( \{a_n\} \) is a bounded sequence, we will proceed step by step: ### Step 1: Define a bounded sequence Since ______ _________ ___ _________ _______ _______ ____ ____.
______ ____ __________ ______ _____ ____ ______ ___ ___ ______.
___ _________ ______ ___ _________.
_____ __________ ____ ________ ___ _____ ________ ________ ______.
____ ________ ___ _____ _____ ______ ______ _____ ______.
_________ ______ _________ ________ ____ __________.
____ ___ __________ _____ ___ __________ ______ ________ _________ ________ ___ ______.
__________ __________ _________ ___ ______ ________ __________ __________ ___ ___ ______ ___.
______ ________ _______ _______ ____ _____ ____ ________ __________ ________ _______.
____ _____ _________ ________ ________ ______ _______.
__________ ___ __________ _____ _____ __________ ___ ___ _______ ___.
_________ _____ __________ ______ _____ ______ _________ ________.
__________ _____ ___ __________ ______ _____ __________ __________ __________.
_______ __________ _____ _________ ______ ________ _________ _______.
______ _______ _________ _________ ______ ______ ________ ________ ____.
________ ________ _______ __________ ____ ____ _________.
_____ ______ _________ ______ _________ ______ ________.
___ _______ ____ ____ _________ ____ ______ ______.
_________ ____ __________ __________ _____ ______ __________.
_______ ________ __________ ________ ______ ______ ______ _____ ______.
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