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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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Solution | Comment 2 of 8 |

Start with a(k) = (1+2+3+...+k)/(1*2*3*...*k).

Simplifying the numerator gives a(k) = (k+1) / (2 * (k-1)!)

Since the denominator is a factorial, it will increase much more rapidly than the numerator, implying the limit of a(k) as k->oo is 0.

  Posted by Brian Smith on 2008-01-07 00:19:47
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