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Sequence of wrong means (Posted on 2011-05-26) Difficulty: 2 of 5
A) Start a sequence with any two real numbers, for the third and successive terms take the mean of all of the previous terms.

B) Same as part A) but take the mean incorrectly as follows: add the numbers together but instead of dividing by the number of terms, divide by one less than the number of terms.

C) Same as part A) and B) but take the mean incorrectly as follows: add the numbers together but instead of dividing by the number of terms, divide by one more than the number of terms.

What happens to the sequence in each case? Generalize further.

  Submitted by Jer    
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Solution: (Hide)
A) x, y, (x+y)/2, (x+y)/2, ...

B) x, y, x+y, x+y, ...

C) x, y, (x+y)/3, (x+y)/3, ...

The terms after the first two become the constant (x+y)/(n+1) where n is the number added to what should be divided by.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
generalized solutionRitesh2011-06-02 19:38:21
Solutioninduction does itAdy TZIDON2011-05-27 05:46:38
Solutionapparently the solutionCharlie2011-05-27 02:04:40
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