The coefficient of x^4 in the expansion of (1+5x+9x^2 +.....∞)(1+x^2 )^(11) is a) 171 b) 172 c) 173 d) 176


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Question Number 32543 by rahul 19 last updated on 27/Mar/18

$T h e c o e f f i c i e n t o f x^{4} i n t h e e x p a n s i o n$ $o f (1 + 5 x + 9 x^{2} + . . . . . \infty) {(1 + x^{2})}^{11} i s$ $a) 171$ $b) 172$ $c) 173$ $d) 176$
	Answered by mrW2 last updated on 27/Mar/18

	$17 \times 1 + 9 \times 11 + 1 \times 55 = 171$ $\Rightarrow a n s w e r a)$
	Commented by rahul 19 last updated on 27/Mar/18

	$t h a n k u b o t h!$
	Commented by MJS last updated on 27/Mar/18

	$(1 + 5 x + 9 x^{2} + 13 x^{3} + 17 x^{4} . . .)$ ${(1 + x^{2})}^{11} = (1 + 11 x^{2} + 55 x^{4} + . . .)$ $like before, pick those who give x^{4}$ $1 \times 55 + 9 \times 11 + 17 \times 1 = 171$
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