If {a_n} is a null sequence, and for each n, b_n is the arithmetic mean of the first n terms of {a_n}, then prove {b_n} is a null sequence.
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Originally Posted by natester If {a_n} is a null sequence, and for each n, b_n is the arithmetic mean of the first n terms of {a_n}, then prove {b_n} is a null sequence. Put then: The first term on the right clearly goes to as goes to . The coefficient of the second term has a finite limit as goes to , but because is a null sequence: which proves that is a null sequence RonL
If fact is then too. Where is an arithmetic sequence.
Originally Posted by ThePerfectHacker If fact is then too. Where is an arithmetic sequence. Which is a corrolary of what the original poster was asked to prove RonL
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