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Question Number 394 by prakash jain last updated on 27/Dec/14
f(x)=Σ_(i=1) ^∞ a_i x^i a_i A constant independent of x Is the below statement correct? lim_(x→0) f(x)=0 If not give an example.
$${f}\left({x}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{i}} {x}^{{i}} \\ $$$${a}_{{i}} \:\:\mathrm{A}\:\mathrm{constant}\:\mathrm{independent}\:\mathrm{of}\:{x} \\ $$$$\mathrm{I}{s}\:\mathrm{the}\:\mathrm{below}\:\mathrm{statement}\:\mathrm{correct}? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{0} \\ $$$$\mathrm{If}\:\mathrm{not}\:\mathrm{give}\:\mathrm{an}\:\mathrm{example}. \\ $$
Commented by 123456 last updated on 27/Dec/14
f(x)=Σ_(i=1) ^∞ i!x^i ?
$${f}\left({x}\right)=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{i}!{x}^{{i}} \:\:\:? \\ $$

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