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#1 Help Me ! » convergence of a sequence » 2011-03-24 05:34:30

MAD
Replies: 1

Hi,

I have a problem in my mind, it is as follows:

We know that the sum of positive integer powers of a number x s.t. x is between 0 and 1 converges to 1/(1-x). Furthermore, assume that we have sequence b_{n} converging to b>0. Let

s_{n} = {sum}_{i=0}^{n}[x^{n-i}*b_{i}]     (in words: s_{n} equals to sum from i=0 to n of the terms x to the n-i multiplied by b_{i})

The question is, does s_{n} converges?{may be helpful: if it converges, it converges to b/(1-x)}.

Thanks.

#2 Re: Exercises » Dividing Polynomials - Mixed Sums » 2011-03-15 02:47:12

MAD

1.x^3 + 2x^2 - 120x = x^3 + 12x^2 - 10x^2 - 120x
                                = x^2(x +12) -10x(x + 12)
                                = (x + 12)(x^2 - 10x)
So, cancelling the terms (x - 12), we get x^2 - 10x.

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