If lim_(x→c) ((a_0 +a_1 (x−c)+a_2 (x−c)^2 +...+a_n (x−c)^n )/((x−c)^n ))=0 then a_0 +a_1 +a_2 +..+a


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Question Number 55634 by gunawan last updated on 01/Mar/19

$If \lim_{x \to c} \frac{a_{0} + a_{1} (x - c) + a_{2} {(x - c)}^{2} + . . . + a_{n} {(x - c)}^{n}}{{(x - c)}^{n}} = 0$ $then a_{0} + a_{1} + a_{2} + . . + a_{n} = . .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 01/Mar/19

	$t = x - c$ $\lim_{t \to 0} \frac{a_{0} + a_{1} t + a_{2} t^{2} + a_{3} t^{3} + . . . + a_{n} t^{n}}{t^{n}}$ $f o r (\frac{0}{0}) f o r m a_{0} = 0$ $\lim_{t \to 0} \frac{a_{1} + 2 a_{2} t + 3 a_{3} t^{2} + . . . + {n a}_{n} t^{n - 1}}{{n t}^{n - 1}}$ $t o m a k e (\frac{0}{0}) f o r m a_{1} \to 0$ $s o i n m y v i e w \underset{i = 0}{\sum^{n}} a_{i} = 0$ $l e t o t h e r s c h e c k . . .$
	Commented by gunawan last updated on 01/Mar/19

	$yes$ $thank you Sir$
	Commented by tanmay.chaudhury50@gmail.com last updated on 01/Mar/19

	$m o s t w e l c o m e . . . p l s c h e c k t h e o t h e r s s o l v e d p r o b l e m o r$ $u p l o a d t h e a n s w e r o n l y . . . n o t d e t a i l s . . .$
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