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Mean Sequence (Posted on 2007-05-23) Difficulty: 2 of 5
In the infinite sequence
a, b, (a + b)/2, (a + 3b)/4, . . .
each term after the second is the arithmetic mean of the two previous terms.

Find the limit of the sequence in terms of real numbers a and b.

No Solution Yet Submitted by Dennis    
Rating: 3.6667 (3 votes)

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Solution spoiler | Comment 1 of 7

answer:   b

proof: lim ((a+z*b)/(z+1) = lim(a/z+b)/(1+!/z)

as z==>infinity  lim(a/z+b)/(1+!/z)=b/1=b


  Posted by Ady TZIDON on 2007-05-23 09:26:29
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