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Limit of the sequence? (Posted on 2008-01-06) |
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What is the limit of the sequence?
a(k) = (1+2+3+...+k)/(1*2*3*...*k)
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Submitted by Chesca Ciprian
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Rating: 2.1667 (6 votes)
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Solution:
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(Hide)
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If we rewrite the a(k) term we can find a(k) = k*(k+1)/(2*k!) and after little transformation the term a(k) = 1/(2*(k-2)!) + 1/((k-1)!). Because 1/k! is "going" to e the answer is e+e/2 = 3*e/2 = 4.077 |
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