Is this a polynomial function?

  • Thread starter MHD93
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  • #1
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f(x) = (x^2)/100 + (x^3)/1000 + (x^4)/10000 + .... till the power infinity
 

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  • #2
Mute
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No. You have an infinite number of terms. That automatically makes it not a polynomial. To show this explicitly for this function, note that your function is just

[tex]f(x) = \sum_{n=2}^\infty \left(\frac{x}{10}\right)^n = \sum_{n=0}^\infty \left(\frac{x}{10}\right)^n - 1 -x[/tex]
which diverges when [itex]|x| \geq 10[/itex] and when |x|/10 < 1 converges to

[tex]f(x) = \frac{1}{1-\frac{x}{10}} - 1 - x[/tex]
 

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