Menu Close

Category: Relation and Functions

let-P-n-X-n-X-n-1-X-2-X-1-R-X-1-prove-that-P-n-have-one-root-x-n-inside-0-2-study-the-sequence-x-n-

Question Number 73052 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{P}_{{n}} ={X}^{{n}} \:+{X}^{{n}−\mathrm{1}} \:+….+{X}^{\mathrm{2}} \:+{X}−\mathrm{1}\:\in{R}\left[{X}\right] \\ $$$$\left.\mathrm{1}\left.\right){prove}\:{that}\:{P}_{{n}} {have}\:{one}\:{root}\:{x}_{{n}} \:{inside}\:\right]\mathrm{0},+\infty\left[\right. \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{sequence}\:{x}_{{n}} \\ $$ Answered…

prove-that-k-1-n-H-k-n-1-H-n-n-and-k-1-n-H-k-2-n-1-H-n-2-2n-1-H-n-2n-

Question Number 73044 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{H}_{{k}} =\left({n}+\mathrm{1}\right){H}_{{n}} −{n} \\ $$$${and}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{H}_{{k}} ^{\mathrm{2}} \:=\left({n}+\mathrm{1}\right){H}_{{n}} ^{\mathrm{2}} \:−\left(\mathrm{2}{n}+\mathrm{1}\right){H}_{{n}} \:+\mathrm{2}{n}…