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Limit of the sequence? (Posted on 2008-01-06) Difficulty: 2 of 5
What is the limit of the sequence? a(k) = (1+2+3+...+k)/(1*2*3*...*k)

See The Solution Submitted by Chesca Ciprian    
Rating: 2.1667 (6 votes)

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re(2): Solution | Comment 6 of 10 |
(In reply to re: Solution by Brian Smith)

>It is considered bad practice to use the sum of a series to prove that a sequence converges to 0.
There exists rigorous proof that if a sum series converges, then its limit must be zero. It is a very valid approach to use it, not bad practice.

>Usually it is required to prove the sequence converges to 0 before calculating the sum of an infinite series.
Testing for a zero limit first just makes it potentially faster to find the sum series when that's the goal.
  Posted by Kurious on 2008-01-07 09:27:06

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