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.

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