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The value of lim(xtooo) ((100)/(1-x^(100...

The value of `lim_(xtooo) ((100)/(1-x^(100))-(50)/(1-x^(50)))` is ___________.

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Verified by Experts

The correct Answer is:
`(25)`
We have `underset(xto1)lim(100)/((1-x^(50))(1+x^(50)))-(50)/(1-x^(50))`
`=underset(xto1)lim(100-500(1+x^(50)))/((1-x^(50))(1+x^(50)))`
`=underset(xto1)lim(50(1-x^(50)))/((1-x^(50))(1+x^(50)))`
`=underset(xto1)lim(50)/(1+x^(100))`
=25
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CENGAGE PUBLICATION-LIMITS-Numerical Value Type
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