El coeficiente del término correspondiente a x en el desarrollo de(Ver Imagen)es ?
El coeficiente del término correspondiente a x en el desarrollo de (Ver Imagen) es :
En resumen
¡Hola! Encontrar el coeficiente del término x<img src="https://tex.z-dn.net/?f=%5Cleft%282%20-%20%5Csqrt%5B4%5D%7B%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%7D%5Cright%29%5E%7B19%7D" />1. Se sabe que por el Teorema binomial que : <img src="https://tex.z-dn.net/?
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9
¡Hola!
Encontrar el coeficiente del término x<img src="https://tex.z-dn.net/?f=%5Cleft%282%20-%20%5Csqrt%5B4%5D%7B%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%7D%5Cright%29%5E%7B19%7D" />1.
Se sabe que por el Teorema binomial que : <img src="https://tex.z-dn.net/?f=%28a%2Bb%29%5En%20%3D%20%5Csum_%7Bk-3%7D%5En%20%5Cdbinom%7Bn%7D%7Bk%7D%2Aa%5E%7Bn-k%7D%2Ab%5E%7Bk%7D" />2.
Sólo tienes que hacer : <img src="https://tex.z-dn.net/?f=a%3D%202%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3Ab%20%3D%20-%5Csqrt%5B4%5D%7B%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%7D%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20n%20%3D%2019" />buscando el término, si : k = 4 (el valor idéntico al índice de "b" para la cancelación del exponente "k").
<img src="https://tex.z-dn.net/?f=T_4%20%3D%20%5Cdbinom%7B19%7D%7B4%7D%2A2%5E%7B19-4%7D%2A%5Cleft%28-%5Csqrt%5B%5Cdiagup%5C%21%5C%21%5C%21%5C%21%5C%214%5D%7B%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%7D%5Cright%29%5E%7B%5Cdiagup%5C%21%5C%21%5C%21%5C%21%5C%214%7D" /><img src="https://tex.z-dn.net/?f=T_4%20%3D%20%5Cdbinom%7B19%7D%7B4%7D%2A2%5E%7B15%7D%2A%5Cleft%28%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%7D%5Cright%29" /><img src="https://tex.z-dn.net/?f=T_4%20%3D%20%5Cdbinom%7B19%7D%7B4%7D%2A%5Cleft%28%5Cdfrac%7Bx%2A2%5E%7B15%7D%7D%7B2%5E%7B13%7D%7D%7D%5Cright%29" /><img src="https://tex.z-dn.net/?f=T_4%20%3D%20%5Cdbinom%7B19%7D%7B4%7D%2A2%5E%7B15-13%7Dx" /><img src="https://tex.z-dn.net/?f=T_4%20%3D%20%5Cdbinom%7B19%7D%7B4%7D%2A2%5E%7B2%7Dx" /><img src="https://tex.z-dn.net/?f=T_4%20%3D%20%5Cdbinom%7B19%7D%7B4%7D%2A4x" /><img src="https://tex.z-dn.net/?f=T_4%20%3D%20%5Cdfrac%7B19%2A%5Cdiagup%5C%21%5C%21%5C%21%5C%21%5C%2118%5E6%2A17%2A%5Cdiagup%5C%21%5C%21%5C%21%5C%21%5C%2116%5E4%7D%7B%5Cdiagup%5C%21%5C%21%5C%21%5C%214%2A%5Cdiagup%5C%21%5C%21%5C%21%5C%213%2A2%2A1%7D%20%2A4x" />[img = 10][img = 11][img = 12][img = 13]Respuesta : El coeficiente del término correspondiente a x en el desarrollo es "15504"__________________________¡Espero haberte ayudado, saludos.
DexteR!
= ).
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Respuesta 2
Recordemos el binomio de Newton
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Chspace%2A%7B3cm%7D%28a%2Bb%29%5En%3D%5Csum_%7Bk%3D0%7D%5E%7Bn%7D%5Cbinom%7Bn%7D%7Bk%7Da%5E%7Bn-k%7Db%5E%7Bk%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BAhora%20veamos%20el%20binomio%20propuesto%7D%5C%5C%20%5C%5C%0A%5Chspace%2A%7B2cm%7D%5Cleft%282-%5Csqrt%5B4%5D%7B%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%7D%5Cright%29%5E%7B19%7D%3D%5Csum_%7Bk%3D0%7D%5E%7B19%7D%5Cbinom%7B19%7D%7Bk%7D2%5E%7B19-k%7D%5Cleft%28-%5Csqrt%5B4%5D%7B%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%7D%5Cright%29%5E%7Bk%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BPara%20que%20solo%20aparezca%20el%20literal%20%7Dx%5Ctexttt%7B%20el%20valor%20de%20%7Dk%5Ctexttt%7B%20debe%20ser%20%7D%5C%5C%204%0A" />
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0At_4%3D%5Cbinom%7B19%7D%7B4%7D2%5E%7B19-4%7D%5Cleft%28-%5Csqrt%5B4%5D%7B%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%7D%5Cright%29%5E%7B4%7D%5C%5C%20%5C%5C%20%5C%5C%0At_4%3D%5Cbinom%7B19%7D%7B4%7D2%5E%7B15%7D%5Cleft%28%5Cdfrac%7Bx%7D%7B2%5E%7B13%7D%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0At_4%3D%5Cbinom%7B19%7D%7B4%7D2%5E%7B15-13%7D~x%5C%5C%20%5C%5C%20%5C%5C%0At_4%3D%5Cbinom%7B19%7D%7B4%7D2%5E%7B2%7D~x%5C%5C%20%5C%5C%20%5C%5C%0At_4%3D%5Cbinom%7B19%7D%7B4%7D%5Ccdot4x%5C%5C%20%5C%5C%20%5C%5C%0At_4%3D%5Cdfrac%7B19%5Ctimes%2018%5Ctimes%2017%5Ctimes%2016%7D%7B1%5Ctimes2%5Ctimes3%5Ctimes4%7D%5Ccdot%204x%5C%5C%20%5C%5C%20%5C%5C%0At_4%3D%5Cdfrac%7B19%5Ctimes%2018%5Ctimes%2017%5Ctimes%2016%7D%7B1%5Ctimes2%5Ctimes3%7D%5Ccdot%20x%5C%5C%20%5C%5C%20%5C%5C%0At_4%3D19%5Ctimes%203%5Ctimes%2017%5Ctimes%2016%5Ccdot%20x%5C%5C%20%5C%5C%20%5C%5C%0At_4%3D15504x" />.