Is f(x) = x²/100 + x³/1000 + x⁴/10000 + ... a polynomial?

[MHD93]

f(x) = (x^2)/100 + (x^3)/1000 + (x^4)/10000 + ... till the power infinity

 

[Mute]

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

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

$$f(x) = \frac{1}{1-\frac{x}{10}} - 1 - x$$