what is the coefficient of x^(50 ) in (1+2x+3x^2 +...+101x^(100) )(1+x+x^2 +...+x^(25) )


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Question Number 214329 by malwan last updated on 05/Dec/24

$w h a t i s t h e c o e f f i c i e n t o f$ $x^{50} i n$ $(1 + 2 x + 3 x^{2} + . . . + 101 x^{100}) (1 + x + x^{2} + . . . + x^{25})$
	Answered by mr W last updated on 05/Dec/24

	$51 + 50 + 49 + . . . + 26$ $= \frac{(51 + 26) \times 26}{2} = 1001 ✓$
	Commented by malwan last updated on 06/Dec/24


	Answered by A5T last updated on 05/Dec/24

	$= 51 + 50 + 49 + . . . + 26 = \frac{51 (52)}{2} - \frac{25 (26)}{2} = 1001$ $. . . + 1001 x^{50} + . . .$
	Commented by malwan last updated on 06/Dec/24

	$t h a n k y o u s i r$
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