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Mathematical Analysis Fundamentals by Agamirza Bashirov

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image

in case when it converges.

Proof

If x1image, then the series in Eq. (3.4) diverges by Corollary 3.27. If x<1image, then from

sn=k=0nxk=1+x+x2++xn=1-xn+11-x,

image

it follows that limnsn=1/(1-x)image.  

Example 3.31

Theorem 3.30 allows us to convert a ...

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