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- Zero to the zero power - Is $0^0=1$? 21 answers
I have a doubt regarding the value of the expression $0^0$. I know this value is taken as indeterminate as far as limits are concerned. All was fine upto now. But when I encountered power series, I found out when $x=a$ in the expression summation $[b (x-a)^n]$ where $n=0$ to infinity, of the power series, then the series always converges which is understood. But what bothers me is its value converges to $b$ and not $0$. That is the first term of the power series is written as $b \cdot 0^0$ and $0^0$ is taken as $1$ and not as indeterminate.
Can anyone tell me why this is so? How is it possible at one time we define $0^0$ as indeterminate and at other time its value is taken as $1$? Could anyone help me on this one? Thanks.