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Question Number 186002 by Shrinava last updated on 30/Jan/23

Commented by JDamian last updated on 30/Jan/23
why did you re-post the same question?
	Answered by mr W last updated on 30/Jan/23

	${l e t}^{'} s f i n d t h e c o e f f i c i e n t o f x^{n} t e r m i n$ ${(1 + x)}^{2 n}, w h i c h i s c l e a r l y C_{n}^{2 n} .$ $o n t h e o t h e r s i d e$ ${(1 + x)}^{2 n} = {(1 + x)}^{n} {(1 + x)}^{n}$ $t h e c o e f . o f x^{n} f r o m {(1 + x)}^{n} {(1 + x)}^{n} i s$ $\underset{k = 0}{\sum^{n}} C_{k}^{n} C_{n - k}^{n} .$ $s i n c e C_{n - k}^{n} = C_{k}^{n}, \underset{k = 0}{\sum^{n}} C_{k}^{n} C_{n - k}^{n} = \underset{k = 0}{\sum^{n}} {(C_{k}^{n})}^{2},$ $t h e r e f o r e$ $\underset{k = 0}{\sum^{n}} {(C_{k}^{n})}^{2} = C_{n}^{2 n} ✓$
	Commented by Shrinava last updated on 30/Jan/23

	$cool dear professor thank you$
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